Question

What is the quotient?

Answer 1

Answer:

Choice B is the answer.

Step-by-step explanation:

We have given an expression.

$\frac{2y^{2}-6y-20 }{4y+12}$ ÷ $\frac{y^{2}+5y+6 }{3y^{2}+18y+27 }$

We have to find the quotient of the given expression.

$\frac{2y^{2}-10y+4y-20 }{4(y+3)}$ ÷ $\frac{y^{2}+2y+3y+6 }{3(y^{2}+6y+9) }$

$\frac{2y(y-5)+4(y-5)}{4(y+3)}$ ÷ $\frac{y(y+2)+3(y+2)}{3(y^{2}+3y+3y+9) }$

$\frac{(2y+4)(y-5)}{4(y+3)}$ ÷ $\frac{(y+2)(y+3)}{3(y+3)(y+3)}$

By changing distribution into multiplication, we have

$\frac{2(y+2)(y-5)}{4(y+3)}$ × $\frac{3(y+3)(y+3)}{(y+2)(y+3)}$

$\frac{3(y-5)}{2}$ which is the answer.