Add and Subtract Rational Expressions with a Common Denominator: example 8.35

$\begin{array}{cccc}& & & \hfill \frac{5x^2-7x+3}{x^2-3x–18}-\frac{4x^2+x-9}{x^2-3x–18}\hfill \\ \\ \\ \begin{array}{c}\text{Subtract the numerators and place the}\hfill \\ \text{difference over the common}\hfill \\ \text{denominator.}\hfill \end{array}\hfill & & & \hfill \frac{5x^2-7x+3-\left(4x^2+x-9\right)}{x^2-3x–18}\hfill \\ \\ \\ \text{Distribute the sign in the numerator.}\hfill & & & \hfill \frac{5x^2-7x+3-4x^2-x+9}{x^2-3x-18}\hfill \\ \\ \\ \text{Combine like terms.}\hfill & & & \hfill \frac{x^2-8x+12}{x^2-3x-18}\hfill \\ \\ \\ \begin{array}{c}\text{Factor the numerator and the}\hfill \\ \text{denominator.}\hfill \end{array}\hfill & & & \hfill \frac{\left(x-2\right)\left(x-6\right)}{\left(x+3\right)\left(x-6\right)}\hfill \\ \\ \\ \text{Simplify by removing common factors.}\hfill & & & \hfill \frac{\left(x-2\right)\cancel{\left(x-6\right)}}{\left(x+3\right)\cancel{\left(x-6\right)}}\hfill \\ \text{Simplify.}\hfill & & & \hfill \frac{\left(x-2\right)}{\left(x+3\right)}\hfill \end{array}$