유리함수

$\begin{array}{cccc} & & & \quad \frac{{p}^{3}-2{p}^{2}+2p-4}{{p}^{2}-7p+10} \\ \\ \\ \begin{array}{c}\text{Factor the numerator and denominator,} \\ \text{using grouping to factor the numerator.}\end{array} & & & \quad \frac{{p}^{2}(p-2)+2(p-2)}{(p-5)(p-2)} \\ & & & \quad \frac{({p}^{2}+2)(p-2)}{(p-5)(p-2)} \\ \\ \\ \begin{array}{c}\text{Remove the common factor of}\,p-2 \\ \text{from the numerator and the denominator.}\end{array} & & & \quad \frac{({p}^{2}+2)(p-2)}{(p-5)(p-2)} \\ & & & \quad \frac{{p}^{2}+2}{p-5}\end{array}$