Chapter 5.6, Problem 15WE

To determine

To simplify the given expression.

Answer to Problem 15WE

  $\frac{a^2-b^2}{ab}$

Explanation of Solution

Given:

Expression: $a{b}^{-1}-a^{-1}b$

Calculation:

Consider the given expression $a{b}^{-1}-a^{-1}b$ ,

It can also be written as $\frac{a}{b}-\frac{b}{a}$ .

Since the denominators of both the fractions are different, find the least common denominator for both the fractions.

Here, least common denominator is $ab$ , so

  $\frac{a}{b}-\frac{b}{a}$

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

  $=\frac{a^2}{ab}-\frac{b^2}{ab}$

Now, as the denominators of the two fractions are same, simply subtract the numerators and put the result on the same denominator.

  $=\frac{a^2-b^2}{ab}$

Conclusion:

Therefore, after simplification, the answer is $\frac{a^2-b^2}{ab}$ .