Chapter 7: Q. 393 (page 735)

In the following exercise, divide.
$\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$

Short Answer

Expert verified

The simplified expression is $\frac{5}{c + 4}$

Step by step solution

Step 1. Given information

Expression is $\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$

Step 2. Rewrite the complex fraction as division

$(\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}) \div (\frac{c^{2} - 4 c - 32}{15 c + 10})$

Step 3. Rewrite as the product of first times the reciprocal of the second.

$(\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}) \times (\frac{15 c + 10}{c^{2} - 4 c - 32})$

Step 4. Factorize the denominator and numerator

$(\frac{(c - 8) (c + 8)}{3 c^{2} + 24 c + 2 c + 16}) \times (\frac{5 (3 c + 2)}{c^{2} - 8 c + 4 c - 32}) = (\frac{(c - 8) (c + 8)}{3 c (c + 8) + 2 (c + 8)}) \times (\frac{5 (3 c + 2)}{c (c - 8) + 4 (c - 8)}) = \frac{(c - 8) (c + 8)}{(3 c + 2) (c + 8)} \times \frac{5 (3 c + 2)}{(c - 8) (c + 4)}$

Step 5.Multiply and remove common factors

$\frac{5 (c - 8) (c + 8) (3 c + 2)}{(3 c + 2) (c + 8) (c - 8) (c + 4)} = \frac{5}{c + 4}$

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In the following exercise, divide.
$\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the complex fraction as division

Step 3. Rewrite as the product of first times the reciprocal of the second.

Step 4. Factorize the denominator and numerator

Step 5.Multiply and remove common factors

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In the following exercise, divide. c2-643c2+26c+16c2-4c-3215c+10

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the complex fraction as division

Step 3. Rewrite as the product of first times the reciprocal of the second.

Step 4. Factorize the denominator and numerator

Step 5.Multiply and remove common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, divide.
$\frac{\frac{c^{2} - 64}{3 c^{2} + 26 c + 16}}{\frac{c^{2} - 4 c - 32}{15 c + 10}}$