Chapter 6.5, Problem 6ST

To determine

Find the simplified form of the given expression.

Answer to Problem 6ST

The simplified form of the expression is $\frac{28b+24}{21a{b}^2}$ .

Explanation of Solution

Given:

The given expression is $\frac{4}{3ab}+\frac{8}{7a{b}^2}$ .

Calculation:

Since the denominators are different, rewrite the fractions using their least common denominator, $21a{b}^2$ .

  $\begin{array}{l}\frac{4}{3ab}+\frac{8}{7a{b}^2}\\ =\frac{4\cdot 7b}{3ab\cdot 7b}+\frac{8\cdot 3}{7a{b}^2\cdot 3}\\ =\frac{28b}{21a{b}^2}+\frac{24}{21a{b}^2}\end{array}$

Useaddition rule of fraction.

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

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

  $=\frac{28b+24}{21a{b}^2}$

Hence the simplified form of the expression is $\frac{28b+24}{21a{b}^2}$ .