Chapter 11.4, Problem 39PPE

To determine

Add or subtract $\frac{r-5}{9+p^3}-\frac{2k+1}{9+p^3}$

Answer to Problem 39PPE

The solution of the given equation is $\frac{r-2k-6}{9+p^3}$

Explanation of Solution

Given:

Given equation

  $\frac{r-5}{9+p^3}-\frac{2k+1}{9+p^3}$

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
1. Multiply both sides of equations by LCD(least common denominator) of all denominators.
2. Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order to solve the equation $\frac{r-5}{9+p^3}-\frac{2k+1}{9+p^3}$ , observe that the LCD of all the denominators is $9+p^3$ . So simplify further as shown below

  $\begin{array}{c}\frac{r-5}{9+p^3}-\frac{2k+1}{9+p^3}=\frac{r-5-\left(2k+1\right)}{9+p^3}\\ =\frac{r-5-2k-1}{9+p^3}\\ =\frac{r-2k-6}{9+p^3}\end{array}$

Thus, the solution of the given equation is $\frac{r-2k-6}{9+p^3}$