Question

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

Answer 1

`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`