Solving rational equations that lead to linear equations

Question

((2x+5)/2)-(3x/(x-2))=x

Answer 1

multiply both sides by the LCM which is 2(x-2)

this yields...

(2x+5)(x-2)-2(3x)=2(x-2)x

2x^2+5x-4x-10-6x=2x^2-4x

cancel the 2x^2 on each side

5x-4x-10-6x=-4x

-5x-10=-4x

-10=5x-4x

-10=x is the solution