Question

Solve for x: (5x - 10)/(x - 2) = (3x)/(x + 1)

Answer 1

(5x-10)/(x-2)-(3x)/(x+1)=0 The (3x)/(x+1) was brought to the other side
Finding a common denominator you get:
[(5x-10)(x+1)-(3x)(x-2)]/(x-2)(x+1)=0
(5x^2-5x-10-3x^2+6x)/(x-2)(x+1) Combine like terms in the numerator
(2x^2+x-10)/(x-2)(x+1)=0 Factor the numerator
(2x+5)(x-2)/(x-2)(x+1)=0 The (x-2) in the numerator and denominator cancel
(2x+5)/(x+1)=0 Multiply both sidesof the equation by (x+1) to eliminate denominator
2x+5=0
2x=-5
x=-5/2