Question

It says to Simplify the expression to lowest terms.
4x^2-9
-------
2x^2+11x+12


I don't understand how to do this.

Answer 1

@dan815

Answer 2

@Compassionate

Answer 3

@wio @skullpatrol

Answer 4

@jim_thompson5910

Answer 5

hint:

factor 4x^2-9 to get (2x-3)(2x+3)

we use the difference of squares rule here

Answer 6

also try to factor 2x^2+11x+12

Answer 7

Is the bottom (x+4) ? so it would be 2x+3/x+4
@jim_thompson5910

Answer 8

not quite

Answer 9

multiply the first coefficient and the last term to get: 2*12 = 24

what two numbers multiply to 24 AND add to 11 (middle coefficient)?

Answer 10

8 and 3?

Answer 11

@jim_thompson5910

Answer 12

so 11x = 8x + 3x

Answer 13

then we factor by grouping

Answer 14

2x^2+11x+12

2x^2+8x+3x+12

(2x^2+8x)+(3x+12)

2x(x + 4) + (3x+12)

2x(x + 4) + 3(x + 4)

(2x + 3)(x + 4)

Answer 15

So that means 2x^2+11x+12 factors to (2x + 3)(x + 4)

Answer 16

oh and nvm, i misread

Answer 17

it looks like you have the right answer

Answer 18

actually, it should be

\[\Large \frac{2x-3}{x+4}\]

Answer 19

not 2x+3 in the numerator

Answer 20

since the 2x+3 terms will cancel

Answer 21

Okay, thanks for the help!

Answer 22

yw