## Algebra: A Combined Approach (4th Edition)

$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{23-5x}{(x-3)(x-2)}$
$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}$ Factor the denominator of the first fraction: $\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{13}{(x-3)(x-2)}-\dfrac{5}{x-3}=...$ Evaluate the substraction of the two rational expressions and simplify: $...=\dfrac{13-5(x-2)}{(x-3)(x-2)}=\dfrac{13-5x+10}{(x-3)(x-2)}=\dfrac{-5x+23}{(x-3)(x-2)}=...$ $...=\dfrac{23-5x}{(x-3)(x-2)}$