Find the product or quotient.
-$$\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }$$
A) $z + 4$
B) $\frac { z } { z ^ { 2 } + 13 z + 42 }$
C) $\frac { \mathrm { z } + 4 } { \mathrm { z } }$
D) $\frac { z + 4 } { z ^ { 2 } + 7 z }$

Question

Quizplus · Accepted Answer

First, factor all the polynomials: $\frac{(z+2)(z+6)}{(z+7)(z+6)} \div \frac{z(z+2)}{(z+7)(z+4)}$. Simplify by flipping the second fraction and multiplying, then cancel common factors to get $\frac{z+4}{z}$.

Find the Product or Quotient z2+8z+12z2+13z+42÷z2+2zz2+11z+28\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }z2+13z+42z2+8z+12​÷z2+11z+28z2+2z​

Find the Product or Quotient $\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }$