How do you solve \frac { x - 1} { x + 3} = \frac { x + 2} { x }?

1 Answer
Jun 14, 2017

x=-1

Explanation:

Since this is set up like a proportion, cross multiply.
(x-1)/(x+3) = (x+2)/x
(x)(x-1)=(x+2)(x+3)

Multiply out both sides, respectively.
(x)(x-1)=(x+2)(x+3)
x^2-x=x^2+3x+2x+6
x^2-x=x^2+5x+6

Begin isolating x to one side by subtracting both sides by x^2.
x^2-x=x^2+5x+6
-x=5x+6

Subtract both sides by 5x to get x all onto the left side.
-x=5x+6
-6x=6

Divide by -6 on both sides to isolate x, leaving you with the solution of the equation.
-6x=6
x=-1