Question

How do you simplify `(4x^2-9)/(2x^2+11x+12)` to lowest terms?

Answer 1

`(2x-3)/(x+4)`

Explanation:

`4x^2-9=(2x-3)(2x+3)`
`2x^2+11x+12= (2x+3)(x+4)`

Therefore,

`(4x^2-9)/(2x^2+11x+12) = ((2x-3)(2x+3))/((2x+3)(x+4))`

= `(2x-3)/(x+4)`

Answer 2

`(2x-3)/(x+4)`

Explanation:

`(4x^2-9)/(2x^2+11x+12)`

=`[(2x-3)(2x+3)]/(2x^2+8x+3x+12)`

=`[(2x-3)(2x+3)]/[2x(x+4)+3(x+4)]`

=`[(2x-3)(2x+3)]/[(x+4)(2x+3]`

=`(2x-3)/(x+4)` , `x!=-4`, `x!=-3/2`