Решение №11875: \(\frac{7a}{(a+b)^{12}}=\frac{7a(a+b)^{2}}{(a+b)^{12}(a+b)^{2}}=\frac{7a(a+b)^{2}}{(a+b)^{14}}\) и \(\frac{9b}{(a+b)^{14}}\)

Ответ: \((a+b)^{14}\)

Решение №11878: \(\frac{10b}{b^{3}-8}=\frac{10b}{(b-2)(b^{2}+2b+4)}\) и \(\frac{1}{b-2}=\frac{b^{2}+2b+4}{(b-2)(b^{2}+2b+4)}=\frac{b^{2}+2b+4}{b^{3}-8}\)

Ответ: \(b^{3}-8\)

Решение №11879: \(\frac{1-5y}{t^{3}+y^{3}}=\frac{1-5y}{(t+y)(t^{2}-ty+y^{2})}\) и \(\frac{t+y}{t^{2}-ty+y}=\frac{(t+y)(t+y)}{(t+y)(t^{2}-ty+y^{2}}=\frac{(t+y)^{2}}{t^{3}+y^{3}}\)

Ответ: \(t^{3}+y^{3}\)

Решение №11883: \(\frac{z^{2}+tz+t^{2}}{zt+z^{2}}=\frac{z^{2}+tz+t^{2}}{z(t+z)}=\frac{(z-t)(z^{2}+tz+t^{2})}{z(t+z)(z-t)}=\frac{z^{3}-t^{3}}{z(z^{2}-t^{2})}\) и \(\frac{3t}{z^{2}-t^{2}}=\frac{3t}{(z-t)(z+t)}=\frac{3tz}{z(z^{2}-t^{2})}\)

Ответ: \(z(z^{2}-t^{2})\)

Решение №11885: \(\frac{m}{(m+n)}=\frac{m^{2}}{m(m+n)}\), \(\frac{n}{m}=\frac{n(m+n)}{m(m+n)}\) и \((m+n)=\frac{m(m+n)(m+n)}{m(m+n)}=\frac{m(m+n)^{2}}{2(m+n)}\)

Ответ: \(2(m+n)\)

Решение №11886: \(3t=\frac{3t \cdot s^{2}t}{s^{2}t}=\frac{3t^{2}s^{2}}{s^{2}t}\), \(\frac{2t}{s^{2}}=\frac{2t \cdot t}{s^{2}t}=\frac{2t^{2}}{s^{2}t}\) и \(\frac{5}{st}=\frac{5s}{st \cdot s}=\frac{5s}{s^{2}t}\)

Ответ: \(s^{2}t\)

Пока решения данной задачи,увы,нет...

Ответ: 4

Решение №11890: \(\frac{c-1}{(c-2)(c+2)}=\frac{c-1}{c^{2}-4}\), \(\frac{c^{2}}{c-2}=\frac{c^{2}(c+2)}{(c-2)(c+2)}=\frac{c^{2}(c+2)}{c^{2}-4}\) и \(\frac{4}{c+2}=\frac{4(c-2)}{(c+2)(c-2)}=\frac{4(c-2)}{c^{2}-4}\)

Ответ: \(c^{2}-4\)

Решение №11895: \(\frac{10xy}{4x^{2}-y^{2}}=\frac{10xy}{(2x-y)(2x+y)}\), \(\frac{2x}{-2x-y}=\frac{2x}{-(2x+y)}=\frac{-2x \cdot (2x-y)}{(2x+y)(2x-y)}=\frac{-2x(2x-y)}{4x^{2}-y^{2}}\) и \(\frac{5y}{y-2x}=\frac{5y}{-(2x-y)}=\frac{-5y \cdot (2x+y)}{(2x-y)(2x+y)}=\frac{-5y(2x+y)}{4x^{2}y^{2}}\)

Ответ: \(4x^{2}y^{2}\)

Решение №11896: \(\frac{6x}{5x^{2}-45}=\frac{6x}{5(x^{2}-9)}=\frac{6x(x+3)(x-3)}{5(x-3)(x+3)(x-3)(x+3)}=\frac{6x(x^{2}-9)}{5(x-3)^{2}(x+3)^{2}}\), \(\frac{(x-3)^{2}}{-x^{2}-6x-9}=\frac{(x-3)^{2}}{-(x^{2}+6x+9)}=\frac{-(x-3)^{2}}{(x+3)^{2}}=\frac{-5(x-3)^{2}(x-3)^{2}}{5(x+3)^{2}(x-3)^{2}}\) и \(\frac{x^{2}+6x+9}{x^{2}+9-6x}=\frac{(x+3)^{2}}{(x-3)^{2}}=\frac{5(x+3)^{2}(x+3)^{2}}{5(x-3)^{2}(x+3)^{2}}=\frac{5(x+3)^{4}}{5(x-3)^{2}(x+3)^{2}}\)

Ответ: \(5(x-3)^{2}(x+3)^{2}\)