Chapter 11.4, Problem 36PPE

To determine

To write two rational expressions with different denominators, find the Least Common Divisor and to add the two expression.

Answer to Problem 36PPE

Expressions: $\frac{7x^2}{x},\text{ and }\frac{5x^3}{4x}$

LCD: $4x$

Sum: $\frac{7x^2}{x}+\frac{5x^3}{4x}=\frac{28x^2+5x^3}{4x}$

Explanation of Solution

Given:

Any two rational expressions.

Concept Used:

To add two rational expressions:

1. Find Least Common Denominator.
2. To rewrite each rational expression with LCD in above step as denominator.
3. Perform addition.

Calculation:

To write two rational expressions with different denominators take the example

  $\frac{7x^2}{x},\text{ and }\frac{5x^3}{4x}$

Now find the Least Common Denominators, as

  $\begin{array}{l}\frac{7x^2}{x}=\frac{7x^2}{x\cdot 1},\text{ and }\\ \frac{5x^3}{4x}=\frac{5x^3}{4\cdot x}\end{array}$

Since,

  $\frac{7x^2}{x}=\frac{7x^2\cdot 4}{x\cdot 4}=\frac{28x^2}{4x}$

Thus, least common denominator is $4x$ .

Now, the above rational expressions can be added as:

  $\begin{array}{c}\frac{7x^2}{x}+\frac{5x^3}{4x}=\frac{28x^2}{4x}+\frac{5x^3}{4x}\left(\begin{array}{l}\text{writtimg each faction}\\ \text{with same LCD}\end{array}\right)\\ =\frac{28x^2+5x^3}{4x}\end{array}$

Thus,

  $\frac{7x^2}{x}+\frac{5x^3}{4x}=\frac{28x^2+5x^3}{4x}$