Question

Para valores de a diferentes de -1, 0 e 1, a expressão (1/a^2 -1)((1-a)/(1+a)-(1+a)/(1-a))(1-a/4) é igual a.

Answer 1

$\left(\frac{1}{a^2}-1\right)\left(\frac{1-a}{1+a}-\frac{1+a}{1-a}\right)\left(1-\frac{a}{4}\right)=\\\\\\\left(\frac{1-a^2}{a^2}\right)\left[\frac{(1-a)^2-(1+a)^2}{(1+a)(1-a)}\right]\left(\frac{4-a}{4}\right)=$

$\left(\frac{1-a^2}{a^2}\right)\left(\frac{1-2a+a^2-1-2a-a^2}{1-a^2}\right)\left(\frac{4-a}{4}\right)=\\\\\\\frac{1}{a^2}\cdot\frac{-4a}{1}\cdot\frac{4-a}{4}=\\\\\\\frac{-4a(4-a)}{4a^2} = \\\\\\\frac{-1(4-a)}{a}\\\\\\\boxed{\frac{a-4}{a}}$

Answer 2

Resposta: a-4 sobre a

Explicação passo-a-passo: