Equations with Fractions

Question

I need help finding the solution to the equation.

x+5 - 8     =0

x        x-1

 

I hope somebody can help.

Answer 1

(x+5)/x-8/(x-1)=0,

(x+5)/x=8/(x-1), cross-multiply:

(x-1)(x+5)=8x,

x²+4x-5=8x,

x²-4x-5=0,

(x-5)(x+1)=0, so x-5=0, x=5; or x+1=0, x=-1.

SOLUTION: x=-1 or 5.