Question

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Answer 1

Answer: x=4, x=-5

Explanation:

`(x)/(x-4)-(4)/(x+5)=(36)/(x^2+x-20)`

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

`(x)/(x-4)\left(x-4\right)\left(x+5\right)-(4)/(x+5)\left(x-4\right)\left(x+5\right)=(36)/(x^2+x-20)\left(x-4\right)\left(x+5\right)`

`(x\left(x-4\right)\left(x+5\right))/(x-4) -(4\left(x-4\right)\left(x+5\right))/(x+5) =(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