Chapter 8: Q. 295 (page 967)

Simplify
In the following exercises, use either method.
$\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}}$

Short Answer

Expert verified

$\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}} = \frac{3 m \cdot n}{n - m}$

Step by step solution

Step 1. Given information

We have been given a complex rational expression $\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}}$ .

We have to simplify it.

Step 2. Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.

$\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}} = \frac{\frac{3 \cdot n}{m \cdot n} + \frac{3 \cdot m}{n \cdot m}}{\frac{1 \cdot n^{2}}{m^{2} \cdot n^{2}} - \frac{1 \cdot m^{2}}{n^{2} \cdot m^{2}}}$

Step 3. Simplify the numerator and denominator.

$\frac{\frac{3 \cdot n}{m \cdot n} + \frac{3 \cdot m}{n \cdot m}}{\frac{1 \cdot n^{2}}{m^{2} \cdot n^{2}} - \frac{1 \cdot m^{2}}{n^{2} \cdot m^{2}}} = \frac{\frac{3 \cdot n + 3 \cdot m}{m \cdot n}}{\frac{1 \cdot n^{2} - 1 \cdot m^{2}}{m^{2} \cdot n^{2}}}$

Step 4. Simplify the numerator and denominator, again

$\frac{\frac{3 \cdot n + 3 \cdot m}{m \cdot n}}{\frac{1 \cdot n^{2} - 1 \cdot m^{2}}{m^{2} \cdot n^{2}}} = \frac{\frac{3 (n + m)}{m \cdot n}}{\frac{n^{2} - m^{2}}{m^{2} \cdot n^{2}}}$

Step 5. Rewrite the complex rational expression as a division problem. Multiply the first times by the reciprocal of the second.

$\frac{\frac{3 (n + m)}{m \cdot n}}{\frac{n^{2} - m^{2}}{m^{2} \cdot n^{2}}} = \frac{3 (n + m)}{m \cdot n} \times \frac{m^{2} \cdot n^{2}}{n^{2} - m^{2}} = \frac{3 (n + m)}{m \cdot n} \times \frac{m^{2} \cdot n^{2}}{(n - m) (n + m)} = \frac{3 m \cdot n}{n - m}$

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Simplify
In the following exercises, use either method.
$\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.

Step 3. Simplify the numerator and denominator.

Step 4. Simplify the numerator and denominator, again

Step 5. Rewrite the complex rational expression as a division problem. Multiply the first times by the reciprocal of the second.

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SimplifyIn the following exercises, use either method.3m+3n1m2−1n2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.

Step 3. Simplify the numerator and denominator.

Step 4. Simplify the numerator and denominator, again

Step 5. Rewrite the complex rational expression as a division problem. Multiply the first times by the reciprocal of the second.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Applied Mathematics

Statistics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify
In the following exercises, use either method.
$\frac{\frac{3}{m} + \frac{3}{n}}{\frac{1}{m^{2}} - \frac{1}{n^{2}}}$