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Serga [27]
2 years ago
12

HELP ME PLEASE REAL ANSWERS ONLY

Mathematics
1 answer:
asambeis [7]2 years ago
8 0

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

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