Answer: x=4, x=-5
Step-by-step explanation:
[tex]\frac{x}{x-4}-\frac{4}{x+5}=\frac{36}{x^2+x-20}[/tex]
Multiply everything by the LCM = (x-4)(x+5):
[tex]\frac{x}{x-4}\left(x-4\right)\left(x+5\right)-\frac{4}{x+5}\left(x-4\right)\left(x+5\right)=\frac{36}{x^2+x-20}\left(x-4\right)\left(x+5\right)[/tex]
[tex]\frac{x\left(x-4\right)\left(x+5\right)}{x-4} -\frac{4\left(x-4\right)\left(x+5\right)}{x+5} =\frac{36\left(x-4\right)\left(x+5\right)}{\left(x-4\right)\left(x+5\right)}[/tex]
Simplify by cancelling out same terms: in the numerators and denominators:
[tex]x\left(x+5\right)-4\left(x-4\right)=36[/tex]
[tex]x^2+x-20=0[/tex]
(x+5)(x-4) = 0
The solution to the quadratic equation is x=4, x=-5
