Chapter 11: Q12. (page 731)

Simplify each expression.
$\frac{\frac{a - 4}{a^{2} + 6 a + 8}}{\frac{a^{2} - 3 a - 4}{a^{2} - a - 6}}$

Short Answer

Expert verified

$\frac{(a - 3)}{(a + 4) (a + 1)}$

Step by step solution

Step 1. Division expression.

Write as a division expression.

$\frac{a - 4}{a^{2} + 6 a + 8} \div \frac{a^{2} - 3 a - 4}{a^{2} - a - 6}$

Step 2. Divide.

To divide, multiply by the reciprocal.

$\frac{a - 4}{a^{2} + 6 a + 8} \cdot \frac{a^{2} - a - 6}{a^{2} - 3 a - 4}$

Step 3. Factor.

Factor the given expression and simplify.

$\frac{(a - 4)}{(a + 2) (a + 4)} \cdot \frac{(a + 2) (a - 3)}{(a - 4) (a + 1)} = \frac{(a - 3)}{(a + 4) (a + 1)}$

Therefore, $\frac{\frac{a - 4}{a^{2} + 6 a + 8}}{\frac{a^{2} - 3 a - 4}{a^{2} - a - 6}}$ can be simplified as $\frac{(a - 3)}{(a + 4) (a + 1)}$ .

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Simplify each expression.
$\frac{\frac{a - 4}{a^{2} + 6 a + 8}}{\frac{a^{2} - 3 a - 4}{a^{2} - a - 6}}$

Short Answer

Step by step solution

Step 1. Division expression.

Step 2. Divide.

Step 3. Factor.

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Simplify each expression.a−4a2+6a+8a2−3a−4a2−a−6

Short Answer

Step by step solution

Step 1. Division expression.

Step 2. Divide.

Step 3. Factor.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

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Calculus

Study anywhere. Anytime. Across all devices.

Simplify each expression.
$\frac{\frac{a - 4}{a^{2} + 6 a + 8}}{\frac{a^{2} - 3 a - 4}{a^{2} - a - 6}}$