Question

Simplify the given expression:
$(3y+12b)(5a-b)÷(y+4b)(25a^2-b^2)$

• 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,
$3(y+4b)(5a-b).\left[\text{Taking 3 as common}\right]$
And the denominator can be written as,
$(y+4b)(5a+b)(5a-b).$
$[\text{using identity:}{a}^2-b^2=(a+b\left)\right(a-b\left)\right]$

$\therefore \frac{(3y+12b)(5a-b)}{(y+4b)(25a^2-b^2)}=\frac{3(y+4b)(5a-b)}{(y+4b)(5a+b)(5a-b)}$
$=\frac{3}{5a+b}$