How do you simplify (4x^2-9)/(2x^2+11x+12)4x292x2+11x+12 to lowest terms?

2 Answers
Apr 24, 2018

(2x-3)/(x+4)2x3x+4

Explanation:

4x^2-9=(2x-3)(2x+3)4x29=(2x3)(2x+3)
2x^2+11x+12= (2x+3)(x+4)2x2+11x+12=(2x+3)(x+4)

Therefore,

(4x^2-9)/(2x^2+11x+12) = ((2x-3)(2x+3))/((2x+3)(x+4))4x292x2+11x+12=(2x3)(2x+3)(2x+3)(x+4)

= (2x-3)/(x+4)2x3x+4

Apr 24, 2018

(2x-3)/(x+4)2x3x+4

Explanation:

(4x^2-9)/(2x^2+11x+12)4x292x2+11x+12

=[(2x-3)(2x+3)]/(2x^2+8x+3x+12)(2x3)(2x+3)2x2+8x+3x+12

= [(2x-3)(2x+3)]/[2x(x+4)+3(x+4)](2x3)(2x+3)2x(x+4)+3(x+4)

= [(2x-3)(2x+3)]/[(x+4)(2x+3](2x3)(2x+3)(x+4)(2x+3]

=(2x-3)/(x+4)2x3x+4 , x!=-4x4, x!=-3/2x32