Divide and simplify.
-$$\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }$$
A) $\frac { z - 7 } { z ^ { 2 } + 9 z }$
B) $z - 7$
C) $\frac { z - 7 } { z }$
D) $\frac { z } { z ^ { 2 } + 16 z + 63 }$

Question

Quizplus · Accepted Answer

First, factor all polynomials: $$\frac{(z+7)(z+2)}{(z+9)(z+7)} \div \frac{z(z+2)}{z^2+2z-63}$$ Simplify to: $$\frac{(z+7)(z+2)}{(z+9)(z+7)} \times \frac{z^2+2z-63}{z(z+2)}$$ Further simplification gives: $$\frac{z-7}{z}$$

Divide and Simplify z2+9z+14z2+16z+63÷z2+2zz2+2z−63\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }z2+16z+63z2+9z+14​÷z2+2z−63z2+2z​

Divide and Simplify $\frac { z ^ { 2 } + 9 z + 14 } { z ^ { 2 } + 16 z + 63 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 2 z - 63 }$