Divide.
-$\frac { z ^ { 2 } + 11 z + 30 } { z ^ { 2 } + 14 z + 48 } \div \frac { z ^ { 2 } + 5 z } { z ^ { 2 } + 12 z + 32 }$
A) $\frac { z + 4 } { z ^ { 2 } + 8 z }$
B) $\frac { z + 4 } { z }$
C) $\frac { z } { z ^ { 2 } + 14 z + 48 }$
D)z + 4

Question

Quizplus · Accepted Answer

First, factor all polynomials: $\frac{(z+5)(z+6)}{(z+6)(z+8)} \div \frac{z(z+5)}{z(z+8)}$. Simplify by flipping the second fraction and multiplying: $\frac{(z+5)(z+6)}{(z+6)(z+8)} \times \frac{z(z+8)}{z(z+5)}$. Cancel common factors to get $\frac{z+6}{z+6} \times \frac{z}{z} = 1$, so the simplified expression is $\frac{z+4}{z}$.

Divide - z2+11z+30z2+14z+48÷z2+5zz2+12z+32\frac { z ^ { 2 } + 11 z + 30 } { z ^ { 2 } + 14 z + 48 } \div \frac { z ^ { 2 } + 5 z } { z ^ { 2 } + 12 z + 32 }z2+14z+48z2+11z+30​÷z2+12z+32z2+5z​

Divide
- $\frac { z ^ { 2 } + 11 z + 30 } { z ^ { 2 } + 14 z + 48 } \div \frac { z ^ { 2 } + 5 z } { z ^ { 2 } + 12 z + 32 }$