Chapter 5.6, Problem 14WE

To determine

To simplify the given expression.

Answer to Problem 14WE

  $\frac{x^2-y^2}{x^3{y}^3}$

Explanation of Solution

Given:

Expression: $\frac{1}{x{y}^3}-\frac{1}{x^{3}y}$

Calculation:

Consider the given expression $\frac{1}{x{y}^3}-\frac{1}{x^{3}y}$ ,

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

Here, least common denominator is $x^3{y}^3$ , so

  $\frac{1}{x{y}^3}-\frac{1}{x^{3}y}$

  $=\frac{1\cdot x^2}{x{y}^3\cdot x^2}-\frac{1\cdot y^2}{x^{3}y\cdot y^2}$

  $=\frac{x^2}{x^3{y}^3}-\frac{y^2}{x^3{y}^3}$

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

  $=\frac{x^2-y^2}{x^3{y}^3}$

Conclusion:

Therefore, after simplification, the answer is $\frac{x^2-y^2}{x^3{y}^3}$.