Question

Solve for x.


`(6)/(x - 3) - (12)/(x + 1) = 1`
Use the digits 0-9 to enter the solution with the greatest value.​

Answer 1

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

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}`