Question

X/(x-2) + (x-1)/(x+1) =-1

Answer 1

x = 0 or x = 1

Explanation:

`(x)/(x-2) + (x-1)/(x+1) =-1\\\\\implies (x(x+1))/((x-2)(x+1)) +((x-1)(x-2))/((x-2)(x+1)) = -1\\\\\implies x(x+1) +(x-1)(x-2) = -(x-2)(x+1)\\\\\implies x^2 +x + x^2 -2x-x+2 = -(x^2-2x+x-2)\\\\\implies 2x^2 -2x+2 = -x^2+x+2\\\\\implies 2x^2 -2x+2 +x^2-x-2 =0\\\\\implies 3x^2 -3x=0\\\\\implies 3x(x -1)=0\\\\\implies 3x=0 \;\;\;or\;\;\;(x-1) = 0\\\\\implies x=0 \;\;\;or\;\;\; x=1`