Question

If 1/x+5 + 1/x = 1/x-4 then find the value of x.

Answer 1

1/x+5 +1/x=1/x-4
=x2-8x-20
we get.
x =10 and x = -2
hope it helps..

Answer 2

{x+(x+5)}/{x(x+5)}=1/(x-4)
(2x+5)/(x²+5x)=1/(x-4)
(2x+5)(x-4)=1(x²+5x)
2x(x-4)+5(x-4)=x²+5x
2x²-8x+5x-20=x²+5x
2x²-x²-8x+5x-5x-20=0
x²-8x-20=0
x²-10x+2x-20=0
x(x-10)+2(x-10)=0
x=10 or x=-2