Question

guided practice
divide: $dfrac{x^2 - 25}{x^2 + 10x + 25} div dfrac{2x + 10}{4x + 20}$
a. $dfrac{2(x - 5)}{x + 5}$
b. $1$
c. $dfrac{x - 5}{x + 5}$
d. $dfrac{(x - 5)}{2(x + 5)}$

Explanation:

Step1: Factor all expressions

$z^2-25=(z-5)(z+5)$, $z^2+10z+25=(z+5)^2$, $2z+10=2(z+5)$, $4z+20=4(z+5)$
Original expression becomes $\frac{(z-5)(z+5)}{(z+5)^2} \div \frac{2(z+5)}{4(z+5)}$

Step2: Change division to multiplication

$\frac{(z-5)(z+5)}{(z+5)^2} \times \frac{4(z+5)}{2(z+5)}$

Step3: Cancel common factors

Cancel $(z+5)$ in numerator/denominator, simplify $\frac{4}{2}=2$
Result: $\frac{2(z-5)}{z+5}$

Answer:

A. $\frac{2(z-5)}{z+5}$