Perform the indicated operation and express in lowest terms.
-$\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

A) $\frac{z-6}{z^{2}+8 z}$

B) $\frac{z}{z^{2}+14 z+48}$

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

D) z - 6

Question

Perform the indicated operation and express in lowest terms.
-$\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$

A) $\frac{z-6}{z^{2}+8 z}$

B) $\frac{z}{z^{2}+14 z+48}$

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

D) z - 6

Quizplus · Accepted Answer

First, factor all polynomials in the numerators and denominators. The given expression simplifies to $\frac{(z+6)(z+3)}{(z+6)(z+8)} \div \frac{z(z+3)}{(z-6)(z+8)}$. When dividing fractions, multiply by the reciprocal of the second fraction: $\frac{(z+6)(z+3)}{(z+6)(z+8)} \times \frac{(z-6)(z+8)}{z(z+3)}$. Simplify by canceling out common factors: $\frac{z-6}{z}$.

Perform the Indicated Operation and Express in Lowest Terms z2+9z+18z2+14z+48÷z2+3zz2+2z−48\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}z2+14z+48z2+9z+18​÷z2+2z−48z2+3z​

Perform the Indicated Operation and Express in Lowest Terms $\frac{z^{2}+9 z+18}{z^{2}+14 z+48} \div \frac{z^{2}+3 z}{z^{2}+2 z-48}$