Question

giải phương trình bậc nhất một ẩn

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

Answer 1

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

<=> \(\frac{x-1}{x+1}-\frac{\left(x-1\right)\left(x+2\right)}{x+1}=\frac{x+1}{x-1}-x-2\)

<=> \(\frac{x-1-\left(x-1\right)\left(x+1\right)}{x+1}=\frac{x+1}{x-1}-x-2\)

<=> \(\frac{-\left(x-1\right)\left(x+2-1\right)}{x+1}=\frac{x+1}{x-1}-x-2\)

<=> -(x - 1) = \(\frac{x+1}{x-1}\) - x - 2

<=> 1 - x = \(\frac{x+1}{x-1}\) - x - 2

<=> 1 = \(\frac{x+1}{x-1}\) - x - 2

<=> x - 1 = x + 1 - 2(x - 1)

<=> x - 1 = -x + 3

<=> x = 3 - x - 1

<=> x = 2 - x

<=> x + x = 2

<=> 2x = 2

<=> x = 1