Perform the indicated operation. Give the answer in lowest terms.
-$\frac{z^{2}+6 z+9}{z^{2}+12 z+27} \div \frac{z^{2}+3 z}{z^{2}+13 z+36}$
A) $\frac{z+4}{z}$
B) $z+4$
C) $\frac{z}{z^{2}+12 z+27}$
D) $\frac{z+4}{z^{2}+9 z}$

Question

Quizplus · Accepted Answer

The expression simplifies to $\frac{z+3}{z+9}$ after factoring and simplifying, which is equivalent to $\frac{z+4}{z}$ when multiplied by the reciprocal of the second fraction.

Perform the Indicated Operation z2+6z+9z2+12z+27÷z2+3zz2+13z+36\frac{z^{2}+6 z+9}{z^{2}+12 z+27} \div \frac{z^{2}+3 z}{z^{2}+13 z+36}z2+12z+27z2+6z+9​÷z2+13z+36z2+3z​

Perform the Indicated Operation $\frac{z^{2}+6 z+9}{z^{2}+12 z+27} \div \frac{z^{2}+3 z}{z^{2}+13 z+36}$