Question

question #5
perform the indicated operation. write the answer in simplest form.
\frac{p^{2}-9p + 18}{p^{2}-11p + 30}cdot\frac{p - 5}{p^{2}+2p - 15}

○ \frac{p + 5}{p - 5}
○ \frac{1}{p + 5}
○ p + 5
○ \frac{p - 5}{p + 5}

Explanation:

Step1: Factor the quadratic expressions

$p^{2}-9p + 18=(p - 3)(p - 6)$; $p^{2}-11p + 30=(p - 5)(p - 6)$; $p^{2}+2p - 15=(p + 5)(p - 3)$

Step2: Rewrite the original expression

The original expression $\frac{p^{2}-9p + 18}{p^{2}-11p + 30}\cdot\frac{p - 5}{p^{2}+2p - 15}=\frac{(p - 3)(p - 6)}{(p - 5)(p - 6)}\cdot\frac{p - 5}{(p + 5)(p - 3)}$

Step3: Cancel out common factors

Cancel out $(p - 3)$, $(p - 6)$ and $(p - 5)$ in the numerator and denominator. We get $\frac{1}{p + 5}$

Answer:

$\frac{1}{p + 5}$