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

$\dfrac{x}{x - 2} + \dfrac{x - 1}{x + 1} = -1$

$(x - 2)(x + 1) \times \dfrac{x}{x - 2} + (x - 2)(x + 1) \times \dfrac{x - 1}{x + 1} = -1(x - 2)(x + 1)$

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

$x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2$

$3x^2 - 3x = 0$

$3x(x - 1) = 0$

$x = 0~~~or~~~x - 1 = 0$

$x = 0 ~~~ or ~~~ x = 1$


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