Question

How do you solve `(x^2-3)/(x+2)=(x-3)/2`?

Answer 1

`x=0,-1`

Explanation:

Solve:

`(x^2-3)/color(blue)((x+2))=(x-3)/color(red)(2)`

Cross multiply.

`color(red)(2)(x^2-3)=color(blue)((x+2))(x-3)`

Expand.

`2x^2-6=(x+2)(x-3)`

FOIL the right side.

`2x^2-6=x^2-3x+2x-6`

Simplify.

`2x^2-6=x^2-x-6`

Add `6` to both sides.

`2x^2-color(red)cancel(color(black)(6))+color(red)cancel(color(black)(6))=x^2-x-color(red)cancel(color(black)(6))+color(red)cancel(color(black)(6))`

Simplify.

`2x^2=x^2-x`

Move all terms to the left side.

`2x^2-x^2+x=0`

Simplify.

`x^2+x=0`

Factor out the `x`.

`x(x+1)=0`

Solutions for `x`.

`x=0`

`x=-1`