Perform the operations. $\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }$
A) $\frac { 2 } { s - 10 }$
B) $\frac { 2 } { s + 4 }$
C) $\frac { 2 } { s + 10 }$
D) $\frac { 2 } { s - 20 }$
E) $\frac { 1 } { s - 10 }$

Question

Quizplus · Accepted Answer

First, we factor all the denominators:
$$s^2-16=(s-4)(s+4)$$
$$s^2-100=(s-10)(s+10)$$
$$s^2-4=(s-2)(s+2)$$
Using these factorizations, we can simplify the expression:
$$\frac{2s^2+12s-80}{s^2-16}\cdot\frac{s-2}{s^2-100}\div\frac{s^2-4}{s^2+6s+8}$$
$$=\frac{2(s-4)(s+10)(s-2)}{(s-4)(s+4)(s-10)(s+2)}\cdot\frac{s-2}{(s-10)(s+10)}\div\frac{(s-2)(s+2)}{(s+2)(s+4)}$$
$$=\frac{2(s+10)}{(s-10)(s+4)}$$
$$=\frac{2}{s-10}\cdot\frac{s+10}{s+4}$$
Therefore, the answer is A.

Perform the Operations 2s2+12s−80s2−16⋅s−2s2−100÷s2−4s2+6s+8\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }s2−162s2+12s−80​⋅s2−100s−2​÷s2+6s+8s2−4​

Perform the Operations $\frac { 2 s ^ { 2 } + 12 s - 80 } { s ^ { 2 } - 16 } \cdot \frac { s - 2 } { s ^ { 2 } - 100 } \div \frac { s ^ { 2 } - 4 } { s ^ { 2 } + 6 s + 8 }$