Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
Equations
The following equation will be solved
[tex]\displaystyle \frac{2}{x+3}-\frac{3}{4-x}=\frac{2x-2}{x^2-x-12}[/tex]
Changing signs of the second term on the left side
[tex]\displaystyle \frac{2}{x+3}+\frac{3}{x-4}=\frac{2x-2}{x^2-x-12}[/tex]
Operating
[tex]\displaystyle \frac{2(x-4)+3(x+3)}{x^2-x-12}=\frac{2x-2}{x^2-x-12}[/tex]
Simplifying denominators, provided
[tex]x^2-x-12\neq 0[/tex]
[tex]2(x-4)+3(x+3)=2x-2[/tex]
Operating
[tex]2x-8+3x+9=2x-2[/tex]
Solving
[tex]\boxed{x=-1}[/tex]
Since
[tex](-1)^2-(-1)-12=-10\neq 0[/tex]
Solution (1)
