Find the product or quotient.
-$$\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }$$
A) $z - 6$

B) $\frac { z } { z ^ { 2 } + 10 z + 24 }$

C) $\frac { z - 6 } { z ^ { 2 } + 4 z }$

D) $\frac { z - 6 } { z }$

Question

Find the product or quotient.
-$$\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }$$
A) $z - 6$

B) $\frac { z } { z ^ { 2 } + 10 z + 24 }$

C) $\frac { z - 6 } { z ^ { 2 } + 4 z }$

D) $\frac { z - 6 } { z }$

Quizplus · Accepted Answer

To divide fractions, multiply by the reciprocal. Factor each polynomial: $(z^2 + 8z + 12) = (z+2)(z+6)$, $(z^2 + 10z + 24) = (z+4)(z+6)$, $(z^2 + 2z) = z(z+2)$, $(z^2 - 2z - 24) = (z-6)(z+4)$. The expression becomes $\frac{(z+2)(z+6)}{(z+4)(z+6)} \times \frac{(z-6)(z+4)}{z(z+2)}$. Cancel common factors: $(z+2)$, $(z+6)$, $(z+4)$. The result is $\frac{z-6}{z}$.

Find the Product or Quotient z2+8z+12z2+10z+24÷z2+2zz2−2z−24\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }z2+10z+24z2+8z+12​÷z2−2z−24z2+2z​

Find the Product or Quotient $\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }$