Question

How do you solve `(3x+2)/(2x-1)=(5x+6)/(x+4)`?

Answer 1

`x = 2` or `x = -1`

Explanation:

Multiply both sides of the equation by `(2x-1)(x+4)` to get:

`(3x+2)(x+4) = (5x+6)(2x-1)`

Multiply out both sides to get:

`3x^2+14x+8 = 10x^2+7x-6`

Subtract the left hand side from both sides to get:

`0 = 7x^2-7x-14`

`color(white)(0) = 7(x^2-x-2)`

`color(white)(0) = 7(x-2)(x+1)`

Hence `x=2` or `x=-1`

It remains to check that neither of these values causes a denominator to become `0`. The only values that do are `x = 1/2` and `x = -4` so we're good.