Question

What is the solution of the equation

Answer 1

`x=-1`

Explanation:

Equations

The following equation will be solved

`\displaystyle (2)/(x+3)-(3)/(4-x)=(2x-2)/(x^2-x-12)`

Changing signs of the second term on the left side

`\displaystyle (2)/(x+3)+(3)/(x-4)=(2x-2)/(x^2-x-12)`

Operating

`\displaystyle (2(x-4)+3(x+3))/(x^2-x-12)=(2x-2)/(x^2-x-12)`

Simplifying denominators, provided

`x^2-x-12\\eq 0`

`2(x-4)+3(x+3)=2x-2`

Operating

`2x-8+3x+9=2x-2`

Solving

`\boxed{x=-1}`

Since

`(-1)^2-(-1)-12=-10\\eq 0`

Solution (1)