Chapter 7: Q. 58 (page 653)

For the following exercises, perform the indicated operations.
$\frac{6 q + 3}{9 q^{2} - 9 q} \div \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$

Short Answer

Expert verified

The solution is $\frac{2 (q + 5)}{9 (q + 11)}$

Step by step solution

Step 1. Given Information

$\frac{6 q + 3}{9 q^{2} - 9 q} \div \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6} = \frac{6 q + 3}{9 q^{2} - 9 q} . \frac{q^{2} + 4 q - 5}{q^{2} + 14 q + 33} . \frac{4 q^{2} + 12 q}{12 q + 6}$

Step 2. Factors the numerator and denominator

$\frac{6 q + 3}{9 q^{2} - 9 q} . \frac{q^{2} + 4 q - 5}{q^{2} + 14 q + 33} . \frac{4 q^{2} + 12 q}{12 q + 6} = \frac{3 (2 q + 1)}{9 q (q - 1)} . \frac{(q + 5) (q - 1)}{(q + 11) (q + 3)} . \frac{4 q (q + 3)}{6 (2 q + 1)}$

Step 3. Multiply the numerators and denominators

$\frac{3 \times 4 q (2 q + 1) (q + 5) (q - 1) (q + 3)}{9 q \times 6 (2 q + 1) (q + 11) (q + 3) (q - 1)} .$

Step 4. Simplify by dividing out common factors

$\frac{2 (q + 5)}{9 (q + 11)}$

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For the following exercises, perform the indicated operations.
$\frac{6 q + 3}{9 q^{2} - 9 q} \div \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerator and denominator

Step 3. Multiply the numerators and denominators

Step 4. Simplify by dividing out common factors

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For the following exercises, perform the indicated operations.6q+39q2-9q÷q2+14q+33q2+4q-5.4q2+12q12q+6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factors the numerator and denominator

Step 3. Multiply the numerators and denominators

Step 4. Simplify by dividing out common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Probability and Statistics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

For the following exercises, perform the indicated operations.
$\frac{6 q + 3}{9 q^{2} - 9 q} \div \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$