Question

Determinati valorile reale ale lui x pentru care suma raporturilor algebrice$\frac{2}{1- x^{2} } si \frac{x}{x-1}$ este egal cu 2

Answer 1

$\frac{2}{1- x^{2} } + \frac{x}{x-1} =2\ \textless \ =\ \textgreater \ \frac{2}{(1-x)(1+x)} - \frac{x}{1-x} =2$
$2-x(1+x)=2(1-x)(1+x)\ \textless \ =\ \textgreater \ 2-x- x^{2} =2-2 x^{2}$
$-x=- x^{2} =\ \textgreater \ x=1$