Chapter 8.5, Problem 31PPSE

Solution

To simplify: The subtraction of $\frac{3}{4x}-\frac{2}{x^2}$ in simplified form and state the restrictions on the variables.

The subtraction of the expression is written as $\frac{3}{4x}-\frac{2}{x^2}=\frac{3x-8}{4x^2}$ where the restriction on variable is $x\ne 0$ .

Given:

The expression to evaluate is $\frac{3}{4x}-\frac{2}{x^2}$ .

Concept used:

Simplify the difference of rational expression by simplifying the expression using the least common denominator and apply the restriction on variables for which the denominator is zero.

Calculation:

With the help of the concept stated above, the subtraction of the expression $\frac{3}{4x}-\frac{2}{x^2}$ is evaluated as:

  $\begin{array}{c}\frac{3}{4x}-\frac{2}{x^2}=\frac{3\cdot x-2\cdot 4}{4x^2}\mathrm{....}\left(\begin{array}{l}\text{ Simplify by least}\\ \text{common denominator}\end{array}\right)\\ =\frac{3x-8}{4x^2}\mathrm{.....}\left(\text{where }x\ne 0\right)\end{array}$

Conclusion:

The subtraction of the expression is written as $\frac{3}{4x}-\frac{2}{x^2}=\frac{3x-8}{4x^2}$ where the restriction on variable is $x\ne 0$ .