Question

Divide $(3y+12b)(5a-b)$by $(y+4b)(25a^2-b^2)$

• A. $\frac{3}{5a+b}$
• B. $\frac{5}{3a+b}$
• C. $=\frac{3}{5a-b}$
• D. $=\frac{3}{a+5b}$

Answer 1

The correct option is A $\frac{3}{5a+b}$

The numerator can be written as $3(y+4b)(5a-b)$
and the denominator can be written as $(y+4b)(5a+b)(5a-b)$ [using identity $a^2-b^2=(a+b)(a-b)$
$\Rightarrow \frac{(3y+12b)(5a-b)}{(y+4b)(25a^2-b^2)}=\frac{3(y+4b)(5a-b)}{(y+4b)(5a+b)(5a-b)}$
$=\frac{3}{5a+b}$