Answer:
Choice B is the answer.
Step-by-step explanation:
We have given an expression.
[tex]\frac{2y^{2}-6y-20 }{4y+12}[/tex] ÷ [tex]\frac{y^{2}+5y+6 }{3y^{2}+18y+27 }[/tex]
We have to find the quotient of the given expression.
[tex]\frac{2y^{2}-10y+4y-20 }{4(y+3)}[/tex] ÷ [tex]\frac{y^{2}+2y+3y+6 }{3(y^{2}+6y+9) }[/tex]
[tex]\frac{2y(y-5)+4(y-5)}{4(y+3)}[/tex] ÷ [tex]\frac{y(y+2)+3(y+2)}{3(y^{2}+3y+3y+9) }[/tex]
[tex]\frac{(2y+4)(y-5)}{4(y+3)}[/tex] ÷ [tex]\frac{(y+2)(y+3)}{3(y+3)(y+3)}[/tex]
By changing distribution into multiplication, we have
[tex]\frac{2(y+2)(y-5)}{4(y+3)}[/tex] × [tex]\frac{3(y+3)(y+3)}{(y+2)(y+3)}[/tex]
[tex]\frac{3(y-5)}{2}[/tex] which is the answer.
