Решение №16987: \(\left ( x+1 \right )\left ( x+2 \right )\left ( x+3 \right )\left ( x+4 \right ); x=\frac{\sqrt{7}-5}{2};=\left (\frac{\sqrt{7}-5}{2}+1 \right )\left ( \frac{\sqrt{7}-5}{2}+2 \right )\left ( \frac{\sqrt{7}-5}{2}+3 \right )\left ( \frac{\sqrt{7}-5}{2}+4 \right )=\left ( \left ( \frac{\sqrt{7}-5}{2} \right )^{2}+5\frac{\sqrt{7}-5}{2}+4 \right )\left ( \left ( \frac{\sqrt{7}-5}{2} \right )^{2}+5\frac{\sqrt{7}-5}{2}+6 \right )=\left ( \frac{-9}{2} \right )^{2}+10\left ( \frac{-9}{2}+24 \right )=-\frac{3}{4}\)

Ответ: \(-\frac{3}{4}\)

Решение №16988: \(\frac{\sqrt[4]{7\sqrt[3]{54}+15\sqrt[3]{128}}}{\sqrt[3]{4\sqrt[4]{32}}+\sqrt[3]{9\sqrt[4]{162}}}=\frac{\sqrt[4]{7\cdot 3\sqrt[3]{2}+15\cdot 4\sqrt[3]{2}}}{\sqrt[3]{4\cdot 2\sqrt[4]{2}}+\sqrt[3]{9\cdot 3\sqrt[4]{2}}}=\frac{\sqrt[4]{81\sqrt[3]{2}}}{2\sqrt[3]{\sqrt[4]{2}}+3\sqrt[3]{\sqrt[4]{2}}}=\frac{3\sqrt[12]{2}}{5\sqrt[12]{2}}=\frac{3}{5}\)

Ответ: \(\frac{3}{5}\)

Решение №16989: \(\frac{x\left | x-3 \right |+x^{2}-9}{2x^{3}-3x^{2}-9x}=\frac{x\left | x-3 \right |+x^{2}-9}{x\left ( 2x^{2}-3x-9 \right )}=\frac{-x\left ( x-3 \right )+x^{2}-9}{x\left ( 2x^{2}-3x-9 \right )};\frac{x\left ( x-3 \right )+x^{2}-9}{x\left ( 2x^{2}-3x-9 \right )}= \frac{3\left ( x-3 \right )}{x\left ( 2x+3 \right )\left ( x-3 \right )};\frac{2x^{2}-3x-9}{x\left ( 2x^{2}-3x-9 \right )}=\frac{3}{x\left ( 2x+3 \right )};\frac{1}{x}\)

Ответ: \(\frac{3}{x\left ( 2x+3 \right )};\frac{1}{x}\)

Решение №16990: \(\frac{5\sqrt[3]{4\sqrt[3]{192}}+7\sqrt[3]{18\sqrt[3]{81}}}{\sqrt[3]{12\sqrt[3]{24}}+6\sqrt[3]{375}}=\frac{5\sqrt[3]{4\cdot 4\sqrt[3]{3}}+7\sqrt[3]{18\cdot 3\sqrt[3]{3}}}{\sqrt[3]{12\cdot 2\sqrt[3]{3}}+6\cdot 5\sqrt[3]{3}}=\frac{31\sqrt[3]{2\sqrt[3]{3}}}{3\sqrt[3]{2\sqrt[3]{3}}}=\frac{31}{3}\)

Ответ: \(\frac{31}{3}\)

Решение №16991: \(\frac{1}{\sqrt{x^{2}+4x+4}}+\left | x-2 \right |=\frac{1}{\sqrt{\left ( x+2 \right )^{2}}}+\left | x-2 \right |=\frac{1}{\left | x+2 \right |}+\left | x-2 \right |=\frac{1+\left | x^{2}-4 \right |}{\left | x+2 \right |}=\frac{1+x^{2}-4}{-\left ( x+2 \right )};\frac{1-\left (x^{2}-4 \right )}{ x+2 };\frac{1+x^{2}-4}{ x+2}=\frac{3-x^{2}}{x+2};\frac{5-x^{2}}{x+2};\frac{x^{2}-3}{x+2}\)

Ответ: \(\frac{3-x^{2}}{x+2};\frac{5-x^{2}}{x+2};\frac{x^{2}-3}{x+2}\)

Решение №16992: \(\frac{\sqrt{x-4\sqrt{x-4}}+2}{\sqrt{x-4\sqrt{x-4}}-2}=\frac{\sqrt{x-4-4\sqrt{x-4}+4}+2}{\sqrt{x-4+4\sqrt{x-4}+4}-2}=\frac{\left | \sqrt{x-4}-2 \right |+2}{\sqrt{x-4}+2-2}=\frac{\left | \sqrt{x-4}-2 \right |+2}{\sqrt{x-4}}=\frac{4}{\sqrt{x-4}}-1;1\)

Ответ: \(\frac{4}{\sqrt{x-4}}-1;1\)

Решение №16993: \(\frac{\sqrt{\left ( 1+\frac{b}{a} \right )^{2}-\frac{4b+1}{a}}\left ( \sqrt{a}+\sqrt{b+\sqrt{a}} \right )^{-\frac{1}{2}}}{\sqrt{a-b+\sqrt{a}}\sqrt{\sqrt{a}-\sqrt{b+\sqrt{a}}}}=\frac{\frac{\sqrt{\left ( a-b \right )^{2}-a}}{a}}{\sqrt{\left ( a-b+\sqrt{a} \right )\left ( a-b-\sqrt{a} \right )}}=\frac{\sqrt{\left ( a-b \right )^{2}-a}}{a\sqrt{\left ( a-b \right )^{2}-a}}=\frac{1}{a}=\frac{1}{2.25}=\frac{1}{\frac{9}{4}}=\frac{4}{9}\)

Ответ: \(\frac{4}{9}\)

Решение №16994: \(\frac{4-\sqrt[3]{a^{2}}}{\left ( 2+\sqrt[3]{ab} \right )^{2}-\left ( \sqrt[3]{a}+2\sqrt[3]{b} \right )^{2}}=\frac{4-\sqrt[3]{a^{2}}}{\left ( 4-\sqrt[3]{a^{2}} \right )-\sqrt[3]{b^{2}\left ( 4-\sqrt[3]{a^{2}} \right )}}=\frac{4-\sqrt[3]{a^{2}}}{\left ( 4-\sqrt[3]{a^{2}} \right )\left ( 1-\sqrt[3]{a^{2}} \right )}=\frac{1}{1-\sqrt[3]{a^{2}}}=\frac{1}{1-\sqrt[3]{0.008}}=\frac{1}{1-0.2}=\frac{1}{0.8}=\frac{5}{4}\)

Ответ: \(\frac{5}{4}\)

Решение №16995: \(\sqrt{\frac{x}{x-a^{2}}}:\left ( \frac{\sqrt{x}-\sqrt{x-a^{2}}}{\sqrt{x}+\sqrt{x-a^{2}}}- \frac{\sqrt{x}+\sqrt{x-a^{2}}}{\sqrt{x}-\sqrt{x-a^{2}}}\right )=\sqrt{\frac{x}{x-a^{2}}}:\left ( \frac{\left ( \sqrt{x}-\sqrt{x-a^{2}} \right )^{2}-\left ( \sqrt{x}+\sqrt{x-a^{2}} \right )^{2}}{\left ( \sqrt{x}+\sqrt{x-a^{2}} \right )\left ( \sqrt{x}-\sqrt{x-a^{2}} \right )} \right )=\sqrt{\frac{x}{x-a^{2}}}:\frac{-4\sqrt{x\left ( x-a^{a} \right )}}{x-x+a^{2}}=-\frac{a^{2}}{4\left ( x-a^{2} \right )}=\frac{a^{2}}{4\left ( a^{2}-x \right )}\)

Ответ: \(\frac{a^{2}}{4\left ( a^{2}-x \right )}\)

Решение №16996: \(\frac{2a^{4}+a^{3}+4a^{2}+a+2}{2a^{3}-a^{2}+a-2}=\frac{\left ( 2a^{4}+2a^{2} \right )+\left ( a^{3}+a \right )+\left ( 2a^{2}+2 \right )}{\left ( 2a^{3}-2a^{2} \right )+\left ( a^{2}-a \right )+\left ( 2a-2 \right )}=\frac{\left ( a^{2}+1 \right )\left ( 2a^{2}+a+2 \right )}{\left ( a-1 \right )\left ( 2a^{2}+a+2 \right )}=\frac{a^{2}+1}{a-1}\)

Ответ: \(\frac{a^{2}+1}{a-1}\)

Решение №16997: \(\frac{a^{3}+a^{2}-2a}{a\left | a+2 \right |-a^{2}+4}=\frac{a\left ( a^{2}-1 \right )+a\left ( a-1 \right )}{a\left | a+2 \right |-a^{2}+4}=\frac{a\left ( a+2 \right )\left ( a-1 \right )}{a\left | a+2 \right |-\left ( a-2 \right )\left ( a+2 \right )}=\frac{+}{}\frac{a\left ( a+2 \right )\left ( a-1 \right )}{a\left ( a+2 \right )-\left ( a-2 \right )\left ( a+2 \right )}=\frac{+}{}\frac{a\left ( a+2 \right )\left ( a-1 \right )}{\left ( a+2 \right )\left ( a-a+2 \right )}=-\frac{a}{2};\frac{a\left ( a-1 \right )}{2}\)

Ответ: \(-\frac{a}{2};\frac{a\left ( a-1 \right )}{2}\)

Решение №16998: \(\left ( \sqrt{ab}-ab\left ( a+\sqrt{ab} \right )^{-1} \right ):\left ( 2\left (\left ( ab \right )^{\frac{1}{2}}-b \right )\left ( a-b \right )^{-1}\right )=\left ( \sqrt{ab}-\frac{ab}{a+\sqrt{ab}} \right ):\frac{2\left ( \sqrt{ab}-b \right )}{a-b}=\left ( \sqrt{ab}-\frac{ab}{\sqrt{a}\left ( \sqrt{a}+\sqrt{b} \right )} \right ):\frac{2\sqrt{b}\left ( \sqrt{a}-\sqrt{b} \right )}{\left ( \sqrt{a}-\sqrt{b} \right )\left ( \sqrt{a}+\sqrt{b} \right )}=\sqrt{ab}\left ( 1-\frac{\sqrt{b}}{\sqrt{a}+\sqrt{b}} \right )\cdot \frac{\sqrt{a}+\sqrt{b}}{2\sqrt{b}}=\frac{a}{2}\)

Ответ: \(\frac{a}{2}\)

Решение №16999: \(\frac{a+1}{2\sqrt[3]{\sqrt{3}-\sqrt{2}}\sqrt[6]{5+2\sqrt{6}}+\frac{1}{a}+a}=\frac{\left ( a+1 \right )a}{2a\sqrt[3]{\sqrt{3}-\sqrt{2}}\sqrt[3]{\sqrt{3}+\sqrt{2}}+1+a^{2}}=\frac{\left ( a+1 \right )a}{2a\sqrt[3]{3-2}+1+a^{2}}=\frac{\left ( a+1 \right )a}{\left ( a+1 \right )^{2}}=\frac{a}{a+1}\)

Ответ: \(\frac{a}{a+1}\)

Решение №17000: \(\frac{\sqrt{2a+2\sqrt{a^{2}-9}}}{\sqrt{2a-2\sqrt{a^{2}-9}}}=\frac{\sqrt{a+3+2\sqrt{\left ( a+3 \right )\left ( a-3 \right )}+a-3}}{\sqrt{a+3-2\sqrt{\left ( a+3 \right )\left ( a-3 \right )}+a-3}}=\frac{\sqrt{a+3}+\sqrt{a-3}}{\sqrt{a+3}-\sqrt{a-3}}=\frac{\left ( \sqrt{a+3}+\sqrt{a-3} \right )^{2}}{\left ( \sqrt{a+3} \right )^{2}-\left ( \sqrt{a-3} \right )^{2}}=\frac{2a+2\sqrt{a^{2}-9}}{6}=\frac{a+\sqrt{a^{2}-9}}{3}\)

Ответ: \(\frac{a+\sqrt{a^{2}-9}}{3}\)

Решение №17001: \(\frac{a^{4}-a^{2}-2a-1}{a^{3}-2a^{2}+1}:\frac{a^{4}+2a^{3}-a-2}{1+\frac{4}{a}+\frac{4}{a^{2}}}=\frac{a^{2}+a+1}{a-1}:\frac{\left ( a+2 \right )\left ( a^{3}-1 \right )a^{2}}{\left ( a+2 \right )^{2}}=\frac{a^{2}+a+1}{a-1}:\frac{\left ( a-1 \right )\left ( a^{2}+a+1 \right )a^{2}}{a+2}=\frac{a^{2}+a+1}{a-1}\cdot \frac{a+2}{\left ( a-1 \right )\left ( a^{2}+a+1 \right )a^{2}}=\frac{a+2}{a^{2}\left ( a-1 \right )^{2}}\)

Ответ: \(\frac{a+2}{a^{2}\left ( a-1 \right )^{2}}\)

Решение №17002: \(\frac{a^{3}-2a^{2}+5a+26}{a^{3}-5a^{2}+17a-13}=\frac{\left ( a^{3}+2a^{2} \right )-\left ( 4a^{2}+8a \right )+\left ( 13a+26 \right )}{\left ( a^{3}-a^{2} \right )-\left ( 4a^{2}-8a \right )+\left ( 13a-13 \right )}=\frac{\left ( a+2 \right )\left ( a^{2}-4a+13 \right )}{\left ( a-1 \right )\left ( a^{2}-4a+13 \right )}=\frac{a+2}{a-1}\)

Ответ: \(\frac{a+2}{a-1}\)

Решение №17003: \(\left ( \frac{x+2b}{x-2b}+\frac{x+2a}{x-2a} \right ):\frac{x}{2}; x=\frac{4ab}{a+b};=\left (\frac{\frac{4ab}{a+b}+2b}{\frac{4ab}{a+b}-2b}+\frac{\frac{4ab}{a+b}+2a}{\frac{4ab}{a+b}-2a} \right ):\frac{4ab}{2\left ( a+b \right )}=\left ( \frac{4ab+2ab+b^{2}}{a+b}:\frac{4ab-2ab-2b^{2}}{a+b}+\frac{4ab+2a^{2}+2ab^{2}}{a+b} :\frac{4ab-2a^{2}-2ab^{2}}{a+b}\right )\frac{a+b}{2ab}=\left ( \frac{3a+b}{a-b}+\frac{3b+a}{b-a} \right )\frac{a+b}{2ab}=\frac{2a-2b}{a-b}\cdot \frac{a+b}{2ab}=\frac{a+b}{ab}\)

Ответ: \(\frac{a+b}{ab}\)

Решение №17004: \(\frac{\frac{\left | b-1 \right |}{b}+b\left | b-1 \right |+2-\frac{2}{b}}{\sqrt{b-2+\frac{1}{b}}}=\frac{\frac{\left | b-1 \right |+b^{2}\left | b-1 \right |+2b-2}{b}}{\sqrt{\frac{b^{2}-2b+1}{b}}}=\frac{\left | b-1 \right |\left ( b^{2}+1 \right )+2\left ( b-1 \right )}{b\sqrt{\frac{\left ( b-1 \right )^{2}}{b}}}=\frac{\left | b-1 \right |\left ( b^{2}+1 \right )+2\left ( b-1 \right )}{\left | b-1 \right |\sqrt{b}}=\frac{b^{2}-1}{\sqrt{b}};\frac{b^{2}+3}{\sqrt{b}}\)

Ответ: \(\frac{b^{2}-1}{\sqrt{b}};\frac{b^{2}+3}{\sqrt{b}}\)

Решение №17005: \(\frac{\frac{a-b}{2a-b}-\frac{a^{2}+b^{2}+a}{2a^{2}+ab-b^{2}}}{\left ( 4b^{4}+4ab^{2}+a^{2} \right ):\left ( 2b^{2}+a \right )}\cdot \left ( b^{2}+b+ab+a \right )=\frac{\frac{a-b}{2a-b}-\frac{a^{2}+b^{2}+a}{\left ( a+b \right )\left ( 2a-b \right )}}{\frac{\left ( 2b^{2}+a \right )^{2}}{2b^{2}+a}}\cdot \left ( b^{2}+b+ab+a \right )=\frac{a^{2}-b^{2}-a^{2}-b^{2}-a}{\left ( a+b \right )\left ( 2a-b \right )\left ( 2b^{2}+a \right )}\cdot \left ( b\left ( b+1 \right )+a\left ( b+1 \right ) \right )=\frac{-\left ( b+1 \right )}{2a-b}=\frac{b+1}{b-2a}\)

Ответ: \(\frac{b+1}{b-2a}\)

Решение №17006: \(\frac{\sqrt{\frac{m+2}{m-2}}+\sqrt{\frac{m-2}{m+2}}}{\sqrt{\frac{m+2}{m-2}}-\sqrt{\frac{m-2}{m+2}}}=\frac{\left ( \sqrt{\frac{m+2}{m-2}}+\sqrt{\frac{m-2}{m+2}} \right )^{2}}{\left ( \sqrt{\frac{m+2}{m-2}} \right )^{2}-\left ( \sqrt{\frac{m-2}{m+2}} \right )^{2}}=\frac{\left ( m+2+m-2 \right )^{2}}{4m+4m}=\frac{4m^{2}}{8m}=\frac{m}{2}\)

Ответ: \(\frac{m}{2}\)

Решение №17007: \(\frac{\sqrt{z^{2}-1}}{\sqrt{z^{2}-1}-z}=\frac{z^{2}-1+z\sqrt{z^{2}-1}}{z^{2}-1-z^{2}}=-\left ( z^{2}+z\sqrt{z^{2}-1}-1 \right )=1-z^{2}-z\sqrt{z^{2}-1}=1-\left ( \frac{1}{2}\left ( \sqrt{m}+\frac{1}{\sqrt{m}} \right ) \right )^{2}-\frac{1}{2}\left ( \sqrt{m}+\frac{1}{\sqrt{m}} \right )\sqrt{\left ( \frac{1}{2}\left ( \sqrt{m}+\frac{1}{\sqrt{m}} \right ) \right )^{2}-1}=\frac{4m-m^{2}-2m-1}{4m}-\frac{m+1}{2\sqrt{m}}\sqrt{\frac{m^{2}-2m+1}{4m}}=\frac{-\left ( m-1 \right )^{2}-\left ( m+1 \right )\left | m-1 \right |}{4m}=\frac{m-1}{2m};\frac{1-m}{2}\)

Ответ: \(\frac{m-1}{2m};\frac{1-m}{2}\)

Решение №17008: \(\frac{\sqrt[3]{m+4\sqrt{m-4}}\sqrt[3]{\sqrt{m-4}+2}}{\sqrt[3]{m-4\sqrt{m-4}}\sqrt[3]{\sqrt{m-4}-2}}\cdot \frac{m-4\sqrt{m-4}}{2}=\frac{\sqrt[3]{\left ( \sqrt{m-4}+2 \right )^{3}}}{\sqrt[3]{\left ( \sqrt{m-4}-2 \right )^{3}}}\cdot \frac{\left ( \sqrt{m-4}-2 \right )^{2}}{2}=\frac{\left ( \sqrt{m-4}+2 \right )\left ( \sqrt{m-4}-2 \right )^{2}}{2\left ( \sqrt{m-4}-2 \right )}=\frac{\left ( \left ( \sqrt{m-4} \right )^{2}-2^{2} \right )}{2}=\frac{m-4-4}{2}=\frac{m-8}{2}\)

Ответ: \(\frac{m-8}{2}\)

Решение №17009: \(\frac{1}{n^{2}+3n+2}=-\frac{1}{n+2}+\frac{1}{n+1};\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{n^{2}+3n+2}=\frac{1}{2}-\frac{1}{n+2}=\frac{n+2-2}{2\left ( n+2 \right )}=\frac{n}{2n+4}\)

Ответ: \(\frac{n}{2n+4}\)

Решение №17010: \(frac{1}{n\left ( n+1 \right )}=\frac{1}{n}-\frac{1}{n+1};1-\frac{1}{n+1}=\frac{n+1-1}{n+1}=\frac{n}{n+1}\)

Ответ: \(\frac{n}{n+1}\)

Решение №17011: \(\frac{\left | r-1 \right |\cdot \left | r \right |}{r^{2}-r+1-\left | r \right |}=\frac{-\left ( r-1 \right )\cdot \left (- r \right )}{r^{2}-r+1+ r };\frac{-\left ( r-1 \right ) r }{r^{2}-r+1- r };\frac{\left ( r-1 \right )r}{r^{2}-r+1-r }=\frac{r^{2}-r}{r^{2}+r};\frac{r}{1-r};\frac{r}{r-1}\)

Ответ: \(\frac{r^{2}-r}{r^{2}+r};\frac{r}{1-r};\frac{r}{r-1}\)

Решение №17012: \(\frac{x^{\frac{1}{6}}-y^{\frac{1}{6}}}{x^{\frac{1}{2}}+x^{\frac{1}{3}}y^{\frac{1}{6}}}\cdot \frac{\left ( x^{\frac{1}{3}}+y^{\frac{1}{3}}-4\sqrt[3]{xy} \right )}{x^{\frac{5}{6}}y^{\frac{1}{3}}-x^{\frac{1}{2}}y^{\frac{2}{3}}}+2x^{-\frac{2}{3}}y^{-\frac{1}{6}}=\frac{x^{\frac{2}{6}}+y^{\frac{2}{6}}}{x^{\frac{5}{6}}y^{\frac{2}{6}}}=\frac{x^{\frac{1}{3}}+y^{\frac{1}{3}}}{\sqrt[6]{x^{5}y^{2}}}\)

Ответ: \(\frac{x^{\frac{1}{3}}+y^{\frac{1}{3}}}{\sqrt[6]{x^{5}y^{2}}}\)

Решение №17013: \(\frac{\left ( x^{\frac{2}{m}}-9x^{\frac{2}{n}} \right )\left ( \sqrt[m]{x^{1-m}}-3\sqrt[n]{x^{1-n}} \right )}{\left ( x^{\frac{1}{m}}+3x^{\frac{1}{n}} \right )^{2}-12x^{\frac{m+n}{mn}}}=\frac{\left ( x^{\frac{1}{m}}-3x^{\frac{1}{n}} \right )\left ( x^{\frac{1}{m}}+3x^{\frac{1}{n}} \right )\left ( x^{\frac{1}{m}-1}-3x^{\frac{1}{n}-1} \right )}{x^{\frac{2}{m}}-6x^{\frac{1}{m}+\frac{1}{n}}+9x\frac{2}{n}}=\frac{\left ( x^{\frac{1}{m}}-3x^{\frac{1}{n}} \right )\left ( x^{\frac{1}{m}}+3x^{\frac{1}{n}} \right )\frac{1}{x}\left ( x^{\frac{1}{m}}-3x^{\frac{1}{n}} \right )}{\left ( x^{\frac{1}{m}}-3x^{\frac{1}{n}} \right )^{2}}=\frac{x^{\frac{1}{m}}+3x^{\frac{1}{n}}}{x}\)

Ответ: \(\frac{x^{\frac{1}{m}}+3x^{\frac{1}{n}}}{x}\)

Решение №17014: \(\left ( \frac{bx+4+\frac{4}{bx}}{2b+\left ( b^{2}-4 \right )x-2bx^{2}}+\frac{\left ( 4x^{2}-b^{2} \right )\cdot \frac{1}{b}}{\left ( b+2x \right )^{2}}-8bx \right )\frac{bx}{2}=\left ( -\frac{bx+2}{\left ( 2x-b \right )bx}+\frac{2x+b}{\left ( 2x-b \right )b} \right )\frac{bx}{2}=-\frac{bx+2}{2\left ( 2x-b \right )}+\frac{\left ( 2x+b \right )x}{2\left ( 2x-b \right )}=\frac{x^{2}-1}{2x-b}\)

Ответ: \(\frac{x^{2}-1}{2x-b}\)

Решение №17015: \(\frac{\left (x^{2}-3x+2 \right )^{-\frac{1}{2}}-\left ( x^{2}+3x+2 \right )^{-\frac{1}{2}}}{\left (x^{2}-3x+2 \right )^{-\frac{1}{2}}+\left ( x^{2}+3x+2 \right )^{-\frac{1}{2}}}-1+\frac{\left ( x^{4}-5x^{2}+4 \right )^{\frac{1}{2}}}{3x}=\sqrt{x^{4}-5x^{2}+4}\frac{\sqrt{x^{2}-3x+2}-\sqrt{x^{2}+3x+2}+\sqrt{x^{2}+3x+2}}{3x\sqrt{x^{2}+3x+2}}=\frac{\sqrt{\left ( x^{2}-3x+2 \right )^{2}}}{3x}=\frac{x^{2}-3x+2}{3}\)

Ответ: \(\frac{x^{2}-3x+2}{3}\)

Решение №17016: \(\left ( \frac{x^{4}+5x^{3}+15x-9}{x^{6}+3x^{4}}+\frac{9}{x^{4}} \right ):\frac{x^{3}-4x+3x^{2}-12}{x^{5}}=\frac{x^{4}+5x^{3}+15x-9+9\left ( x^{2}+3 \right )}{x^{4}\left ( x^{2}+3 \right )}:\frac{\left ( x^{2}-4 \right )\left ( x+3 \right )}{x^{5}}=\frac{\left ( x+3 \right )\left ( x+2 \right )\left ( x^{2}+3 \right )}{x^{4}\left ( x^{2}+3 \right )}\cdot \frac{x^{5}}{\left ( x-2 \right )\left ( x+2 \right )\left ( x+3 \right )}=\frac{x}{x-2}\)

Ответ: \(\frac{x}{x-2}\)