Question

Solve for x.

Answer 1

Answer:

$\boxed{x=5},x=-9$

Step-by-step explanation:

To rid the denominators, multiply both sides by $(x-3)(x+1)$.

We get:

$6(x+1)-12(x-3)=(x-3)(x+1)$

Simplifying, we have:

$6x+6-12x+36=x^2-3x+x-3,\\-6x+42=x^2-2x-3,\\x^2+4x-45=0$

Solving, we get:

$x^2+4x-45=0,\\(x-5)(x+9)=0,\\x=5,x=-9$

Therefore, the solution with the greatest value is $x=\boxed{5}$