Chapter 6.5, Problem 18WE

To determine

Find the simplified form of the given expression.

Answer to Problem 18WE

The simplified form of the expression is $\frac{8b-6}{a{b}^2}$ .

Explanation of Solution

Given:

The given expression is $\frac{8}{ab}-\frac{6}{a{b}^2}$ .

Calculation:

Since the denominators are different, rewrite the fractions using their least common denominator, $a{b}^2$ .

  $\begin{array}{l}\frac{8}{ab}-\frac{6}{a{b}^2}\\ =\frac{8\cdot b}{ab\cdot b}-\frac{6}{a{b}^2}\\ =\frac{8b}{a{b}^2}-\frac{6}{a{b}^2}\end{array}$

Usesubtraction rule of fraction.

  $\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}$

To subtract fractions with the same denominator, subtract their numerators and write the result over the common denominator.

  $=\frac{8b-6}{a{b}^2}$

Hence the simplified form of the expression is $\frac{8b-6}{a{b}^2}$ .