Question

tional expressions: problem 5
perform the operation and simplify if possible. assume all cancelled factors are not zero.
\\(\frac{s^{2}-36}{25}\cdot\frac{s^{2}+4s - 12}{s^{2}+12s + 36}=\\)
enter the simplified expression. do not try to enter its restricted domain.
attempt(s) remaining before you will receive a new version of this problem.
learn partial credit on this problem.

Explanation:

Step1: Factor the expressions

$ s^{2}-36=(s + 6)(s - 6)$; $s^{2}+4s - 12=(s + 6)(s - 2)$; $s^{2}+12s + 36=(s + 6)^{2}$

Step2: Substitute the factored - forms into the original expression

$\frac{s^{2}-36}{25}\cdot\frac{s^{2}+4s - 12}{s^{2}+12s + 36}=\frac{(s + 6)(s - 6)}{25}\cdot\frac{(s + 6)(s - 2)}{(s + 6)^{2}}$

Step3: Cancel out the common factors

Cancel out the common factor $(s + 6)$ in the numerator and denominator. We get $\frac{(s - 6)(s - 2)}{25}=\frac{s^{2}-2s-6s + 12}{25}=\frac{s^{2}-8s + 12}{25}$

Answer:

$\frac{s^{2}-8s + 12}{25}$