Question

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Answer 1

Answer: x=4, x=-5

Step-by-step explanation:

$\frac{x}{x-4}-\frac{4}{x+5}=\frac{36}{x^2+x-20}$

Multiply everything by the LCM = (x-4)(x+5):

$\frac{x}{x-4}\left(x-4\right)\left(x+5\right)-\frac{4}{x+5}\left(x-4\right)\left(x+5\right)=\frac{36}{x^2+x-20}\left(x-4\right)\left(x+5\right)$

$\frac{x\left(x-4\right)\left(x+5\right)}{x-4} -\frac{4\left(x-4\right)\left(x+5\right)}{x+5} =\frac{36\left(x-4\right)\left(x+5\right)}{\left(x-4\right)\left(x+5\right)}$

Simplify by cancelling out same terms: in the numerators and denominators:

$x\left(x+5\right)-4\left(x-4\right)=36$

$x^2+x-20=0$

(x+5)(x-4) = 0

The solution to the quadratic equation is x=4, x=-5