Question

Solve the following equation. Show all your work.

Start Fraction x over x minus 2 End Fraction plus Start Fraction x minus 1 over x plus 1 End Fraction equals negative 1

someone...please..god..

Answer 1

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


`(x - 2)(x + 1) * (x)/(x - 2) + (x - 2)(x + 1) * (x - 1)/(x + 1) = -1(x - 2)(x + 1)`


`(x + 1)x + (x - 2)(x - 1) = -1(x - 2)(x + 1)`


`x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2`


`3x^2 - 3x = 0`


`3x(x - 1) = 0`


`x = 0~~~or~~~x - 1 = 0`


`x = 0 ~~~ or ~~~ x = 1`


Since neither 0 nor 1 cause a zero in a denominator in the original equation, 0 and 1 are acceptable as solutions.

Answer: x = 0 or x = 1