Chapter 7: Q. 56 (page 653)

For the following exercises, perform the indicated operations.
$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$

Short Answer

Expert verified

The simplified expression is $\frac{(n + 8) (n - 1)}{3 n (n - 5) (9 n - 2)} .$

Step by step solution

Step 1. Given Information

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6} = \frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} . \frac{n + 6}{108 n^{2} - 24 n}$

Step 2. Factor numerators and denominators

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} . \frac{n + 6}{108 n^{2} - 24 n} = \frac{4 n (n + 8)}{3 n + 2} . \frac{(n - 1) (3 n + 2)}{(n + 6) (n - 5)} . \frac{n + 6}{12 n (9 n - 2)}$

Step 3. Multiply numerators and denominators

$= \frac{4 n (n + 8) (n - 1) (3 n + 2) (n + 6)}{12 n (n + 6) (n - 5) (3 n + 2) (9 n - 2)} .$

Step 4. Remove common factors

$= \frac{(n + 8) (n - 1)}{3 n (n - 5) (9 n - 2)} .$

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For the following exercises, perform the indicated operations.
$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor numerators and denominators

Step 3. Multiply numerators and denominators

Step 4. Remove common factors

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For the following exercises, perform the indicated operations.4n2+32n3n+2.3n2-n-2n2+n-30÷108n2-24nn+6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor numerators and denominators

Step 3. Multiply numerators and denominators

Step 4. Remove common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

For the following exercises, perform the indicated operations.
$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$