Chapter 11.2, Problem 49PPE

To determine

Simplify the complex fraction: $\frac{\frac{z-10}{z+10}}{3z^2-30z}$

Answer to Problem 49PPE

  $\frac{\frac{z-10}{z+10}}{3z^2-30z}=\frac{1}{3z(z+10)}$

Explanation of Solution

Given:

Simplify the complex fraction: $\frac{\frac{z-10}{z+10}}{3z^2-30z}$

Concept Used:

Find the factors of numerator and denominator, and then cancel the common factor and simplify.

For division of rational expression, we always flip the 2^nd expression and put a multiplication sign.

Rule: $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}·\frac{d}{c}$

Calculation:

  $\begin{array}{l}\frac{\frac{z-10}{z+10}}{3z^2-30z}=\frac{z-10}{z+10}÷\frac{3z^2-30z}{1}\\ \\ \frac{z-10}{z+10}·\frac{1}{3z^2-30z}=\frac{z-10}{z+10}·\frac{1}{3z(z-10)}\\ \\ \frac{z-10}{z-10}·\frac{1}{3z(z+10)}=\frac{1}{3z(z+10)}\end{array}$

Thus, $\frac{\frac{z-10}{z+10}}{3z^2-30z}=\frac{1}{3z(z+10)}$