Q. 269 In the following exercises, simp... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 269 (page 966)

In the following exercises, simplify.
$\frac{2 - \frac{2}{a + 3}}{\frac{1}{a + 3} + \frac{a}{2}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{4}{a + 1} .$

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{2 - \frac{2}{a + 3}}{\frac{1}{a + 3} + \frac{a}{2}}$

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B} 梅 \frac{C}{D} = \frac{A}{B} 路 \frac{D}{C}$

Step 3. Rewrite the expression.

Simplify the numerator and denominator.

$= \frac{\frac{2 (a + 3) - 2}{a + 3}}{\frac{2 + a (a + 3)}{2 (a + 3)}} = \frac{\frac{2 a + 6 - 2}{a + 3}}{\frac{2 + a^{2} + 3 a)}{2 (a + 3)}} = \frac{\frac{2 a + 4}{a + 3}}{\frac{a^{2} + 3 a + 2}{2 (a + 3)}} = \frac{2 a + 4}{a + 3} 梅 \frac{a^{2} + 3 a + 2}{2 (a + 3)}$

Step 4. Simplify the expression.

Rewrite as the product of first times the reciprocal of the second. $= \frac{2 a + 4}{a + 3} 路 \frac{2 (a + 3)}{a^{2} + 3 a + 2} = \frac{2 a + 4}{a + 3} 路 \frac{2 (a + 3)}{a^{2} + 2 a + a + 2} = \frac{2 (a + 2)}{a + 3} 路 \frac{2 (a + 3)}{a (a + 2) + 1 (a + 2)} = \frac{2 (a + 2)}{a + 3} 路 \frac{2 (a + 3)}{(a + 2) (a + 1)} = \frac{4}{a + 1}$

Step 5. Conclusion.

The simplified form of the given expression is $\frac{4}{a + 1}$ .

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91影视

In the following exercises, simplify.
$\frac{2 - \frac{2}{a + 3}}{\frac{1}{a + 3} + \frac{a}{2}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept.

Step 3. Rewrite the expression.

Step 4. Simplify the expression.

Step 5. Conclusion.

One App. One Place for Learning.

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91影视

In the following exercises, simplify.2-2a+31a+3+a2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept.

Step 3. Rewrite the expression.

Step 4. Simplify the expression.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Decision Maths

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{2 - \frac{2}{a + 3}}{\frac{1}{a + 3} + \frac{a}{2}}$