What is the solution of the equation

Question

asked Jul 8, 2021 211k views

1 Answer

Jorge De Los Santos · Answer 1 · 2021-07-14T07:15:39+0000

Answer:

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)