Question

Ajuda aew, tá valendo!! ​

Answer 1

Resposta: $m^2 + n^2$

Explicação passo-a-passo:

A = $\frac{\frac{m^2}{n^2} - \frac{n^2}{m^2}}{\frac{1}{m^2} + \frac{2}{m.n} + \frac{1}{n^2}} . [\frac{(m - n)^2}{(m^2 - n^2)}]^{-1}$  ⇒

A = $\frac{\frac{m^4}{m^2n^2} - \frac{n^4}{m^2n^2}}{(\frac{1}{m} + \frac{1}{n})^2} . [\frac{(m - n)^2}{(m^2 - n^2)}]^{-1}$  ⇒

A = $\frac{\frac{(m^2 + n^2)(m^2 - n^2)}{(mn)^2}}{\frac{(m + n)^2}{(mn)^2}} . [\frac{(m - n)(m - n)}{(m + n)(m - n)}]^{-1}$⇒

A = $\frac{(m^2 + n^2)(m - n)}{(m + n)} . [\frac{(m - n)}{(m + n)}]^{-1}$ ⇒

A = $\frac{(m^2 + n^2)(m - n)}{(m + n)} . \frac{(m + n)}{(m - n)}$  ⇒

A = $m^2 + n^2$

Abraços!