How do I solve:
x^2-1 4x^2
_______ x ________
12x^2+24x x^2+x
1. You can't solve this term. You only can simplify it a bit.
2. The domain of this term is $\displaystyle x\in \mathbb{R} \setminus \{-2, -1\}$
3. Factorize the numerators and the denominators:
$\displaystyle \dfrac{x^2-1}{12x^2+24x} \cdot \dfrac{4x^2}{x^2+x}= \dfrac{(x+1)(x-1)}{12x(x+2)} \cdot \dfrac{4x^2}{x(x+1)} = \dfrac{4x^2(x+1)(x-1)}{12x^2(x+1)(x+2)}$ ........... Cancel like terms:
$\displaystyle result=\dfrac{x-1}{3(x+2)}$