Simplify the expression:
2x^2+9x+4 / x^2+x-6 divided by x^2+6x+8/ 2x^2-5x+2
and give your answer in the form of f(x)/g(x)
your answer for the function f(x) is:________
your answer for the function g(x) is:________
Simplify the expression:
2x^2+9x+4 / x^2+x-6 divided by x^2+6x+8/ 2x^2-5x+2
and give your answer in the form of f(x)/g(x)
your answer for the function f(x) is:________
your answer for the function g(x) is:________
Factor everything first.
$\displaystyle \frac{\frac{(2x+1)(x+4)}{(x+3)(x-2)}}{\frac{(x+4)(x+2)}{(2x-1)(x-2)}}$
Cancel out common factors.
$\displaystyle \frac{\frac{2x+1}{x+3}}{\frac{x+2}{2x-1}}$
Flip and multiply
$\displaystyle \frac{2x+1}{x+3}\cdot\frac{2x-1}{x+2}=\boxed{\frac{4x^2-1}{x^2+5x+6}}$