Chapter 8: Q. 275 (page 966)

Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify.
$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{c (c + 1)}{c - d^{2}}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is $c d$ . Clear the fractions by multiplying the numerator and denominator by that LCD.

$= \frac{c d \cdot (\frac{c}{d} + \frac{1}{d})}{c d \cdot (\frac{1}{d} - \frac{d}{c})} = \frac{c d \cdot \frac{c}{d} + c d \cdot \frac{1}{d}}{c d \cdot \frac{1}{d} - c d \cdot \frac{d}{c}} = \frac{c^{2} + c}{c - d^{2}} = \frac{c (c + 1)}{c - d^{2}}$

Step 3. Conclusion.

The simplified form of the given expression is $\frac{c (c + 1)}{c - d^{2}}$ .

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Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify.
$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

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Simplify a Complex Rational Expression by Using the LCD.In the following exercises, simplify.cd+1d1d-dc

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Statistics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify.
$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$