Question

determine os valores reais de x para que se tenha 2/x2-1 - x/x-1 =1

Answer 1

$\frac{2}{ x^{2} -1} - \frac{x}{x-1} =1 \\ \\ \frac{2}{ x^{2} -1} - \frac{x.(x+1)}{x^{2} -1} = \frac{ x^{2} -1}{x^{2} -1 } \\ \\ 2-( x^{2} +x)= x^{2} -1 \\ \\ 2- x^{2} -x= x^{2} -1 \\ \\ -2 x^{2} -x+3=0 \\ \\ 2 x^{2} +x-3=0 \\ \\ delta=1+4.3.2 \\ \\ delta=25 \\ \\ x'= \frac{-1+5}{4}= \frac{4}{4}=1 \\ \\ x''= \frac{-1-5}{4}= -\frac{6}{4}= -\frac{3}{2}$