Question

Solve the equation. StartFraction x Over x squared minus 1 EndFraction minus StartFraction x plus 6 Over x squared minus x EndFraction equalsStartFraction negative 6 Over x squared plus x EndFraction
Select the correct choice below and fill in any answer boxes in your choice.

A. The solution set is StartSet nothing EndSet . ​(Simplify your​ answer.)
B. There is no solution.

Answer 1

Answer:

$x=-12$.

Step-by-step explanation:

We have been given an equation $\frac{x}{x^2-1}-\frac{x+6}{x^2-x}=-\frac{6}{x^2+x}$. We are asked to solve the given equation.

Upon rewriting the equation, we will get:

$\frac{x}{(x+1)(x-1)}-\frac{x+6}{x(x-1)}=-\frac{6}{x(x+1)}$

Multiply both sides of equation by $x(x+1)(x-1)$:

$\frac{x}{(x+1)(x-1)}*x(x+1)(x-1)-\frac{x+6}{x(x-1)}*x(x+1)(x-1)=-\frac{6}{x(x+1)}*x(x+1)(x-1)$

$x*x-(x+6)(x+1)=-6(x-1)$

$x^2-(x^2+x+6x+6)=-6x+6$

$x^2-x^2-x-6x-6=-6x+6$

$-7x-6=-6x+6$

$-7x-6+6=-6x+6+6$

$-7x=-6x+12$

$-7x+6x=-6x+6x+12$

$-x=12$

$\frac{-x}{-1}=\frac{12}{-1}$

$x=-12$

Therefore, $x=-12$ is the solution of our given equation.