Question 29420
x/(x-2) - (x+1)/x = 8/(x^2-2x) ----(1)
x/(x-2) - (x+1)/x = 8/x(x-2)
Multiplying by x(x-2) through out
xX(x)-(x+1)(x-2)= 8
x^2-[x(x-2)+1(x-2)] = 8
x^2-[x^2-2x+x-2] = 8
x^2-x^2+2x-x+2 = 8
x+2 = 8 
x = 8-2 = 6
Answer: x = 6
Verification:x= 6 in (1)
LHS = 6/4-7/6 = (18-14)/12 =4/12= 1/3
RHS = 8/(36-12) = 8/24 = 1/3 =LHS