Question

How do I simplify ((3x^2+12x+12)/(2x^2+x-6))/((4x^2-9)/(3x^3+x^2-10))

Answer 1

$\dfrac{ \frac{3x^2+12x+12}{2x^2+x-6} }{ \frac{4x^2-9 }{3x^3+x^2-10} } =$

$= \dfrac{3(x + 2)^2}{(2x - 3)(x + 2)} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} }$

$= \dfrac{3(x + 2)}{2x - 3} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} }$

$= \dfrac{3(x + 2)(3x^3+x^2-10) }{(2x - 3)^2(2x + 3)}$