Solve the system of equation 4x/(x^2-25) + 2/(x-5) = 1/(x+5)

Question

Can someone explain how to solve the system of equation 4x/(x^2-25) + 2/(x-5) = 1/(x+5). Is there is solution or no solutions?

Answer 1

4x/(x^2-25)+ 2/(x-5) =1/(x+5)

put over LCD= x^2-25

(4x + 2x +10)/(x^2 -25)= (x-5)/(x^2 -25)

(5x+15)/(x^2-25)=0, set numerator = 0 and solve for x

x=-3

check the answers, plug -3 for x in the original equation

-12/-16 - 1/4 = 1/2

3/4 - 1/4 = 1/2 It works, x=-3