How do you simplify (x^2-2x-3)/(x^2-7x+12)?

Aug 18, 2017

See a solution process below:

Explanation:

First, we can factor the numerator and denominator as follows:

$\frac{\left(x - 3\right) \left(x + 1\right)}{\left(x - 3\right) \left(x - 4\right)}$

We can now cancel common terms in the numerator and denominator:

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}} \left(x + 1\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}} \left(x - 4\right)} \implies \frac{x + 1}{x - 4}$

However, from the original expression we need to ensure we don't divide by $0$.

$\frac{x + 1}{x - 4}$ Where $x - 4 \ne 0$ and $x - 3 \ne 0$

Or

$\frac{x + 1}{x - 4}$ Where $x \ne 4$ and $x \ne 3$