Chapter 11.3, Problem 71MR

To determine

To simplify:

  $\frac{7}{12y}-\frac{1}{12y}$

Answer to Problem 71MR

  $\frac{7}{12y}-\frac{1}{12y}=\frac{1}{2y}$

Explanation of Solution

Given:

  $\frac{7}{12y}-\frac{1}{12y}$

Concept Used:

• Addition/subtraction of two rational expressions with equal numerator is done as:

  $\frac{P\left(x\right)}{R\left(x\right)}\pm \frac{Q\left(x\right)}{R\left(x\right)}=\frac{P\left(x\right)\pm Q\left(x\right)}{R\left(x\right)},R\left(x\right)\ne 0$

Calculation:

In order to simplify:

  $\frac{7}{12y}-\frac{1}{12y}$

Use the formula:

  $\frac{P\left(x\right)}{R\left(x\right)}\pm \frac{Q\left(x\right)}{R\left(x\right)}=\frac{P\left(x\right)\pm Q\left(x\right)}{R\left(x\right)}$

As,

  $\begin{array}{c}\frac{7}{12y}-\frac{1}{12y}=\frac{7-1}{12y}\\ =\frac{6}{12y}\end{array}$

Again simplify the fraction by canceling the common factor of numerator and denominator, as

  $\begin{array}{c}\frac{6}{12y}=\frac{6}{6\times 2y}\\ =\frac{1}{2y}\end{array}$

Thus,

  $\frac{7}{12y}-\frac{1}{12y}=\frac{1}{2y}$