Chapter 7: Q.394 (page 735)

In the following exercise, divide.
$\frac{8 a^{2} + 16 a}{a - 4} . \frac{a^{2} + 2 a - 24}{a^{2} + 7 a + 10} \div \frac{2 a^{2} - 6 a}{a + 5}$

Short Answer

Expert verified

The simplified expression is

$\frac{4 (a + 6)}{(a - 3)}$

Step by step solution

Step 1. Given information

expression to divide is

$\frac{8 a^{2} + 16 a}{a - 4} . \frac{a^{2} + 2 a - 24}{a^{2} + 7 a + 10} \div \frac{2 a^{2} - 6 a}{a + 5}$

Step 2. Rewrite as the product of first times the reciprocal of the second.

$\frac{8 a^{2} + 16 a}{a - 4} . \frac{a^{2} + 2 a - 24}{a^{2} + 7 a + 10} . \frac{a + 5}{2 a^{2} - 6 a}$

Step 3. Factorize the denominator and numerator

$\frac{8 a (a + 2)}{a - 4} . \frac{a^{2} + 6 a - 4 a - 24}{a^{2} + 5 a + 2 a + 10} . \frac{a + 5}{2 a (a - 3)} = \frac{8 a (a + 2)}{a - 4} . \frac{a (a + 6) - 4 (a + 6)}{a (a + 5) + 2 (a + 5)} . \frac{a + 5}{2 a (a - 3)} = \frac{8 a (a + 2)}{a - 4} . \frac{(a - 4) (a + 6)}{(a + 2) (a + 5)} . \frac{a + 5}{2 a (a - 3)}$

Step 4.Multiply and remove common factors

$\frac{8 a (a + 2) (a - 4) (a + 6) (a + 5)}{2 a (a - 4) (a + 2) (a + 5) (a - 3)} = \frac{4 (a + 6)}{a - 3}$

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In the following exercise, divide.
$\frac{8 a^{2} + 16 a}{a - 4} . \frac{a^{2} + 2 a - 24}{a^{2} + 7 a + 10} \div \frac{2 a^{2} - 6 a}{a + 5}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite as the product of first times the reciprocal of the second.

Step 3. Factorize the denominator and numerator

Step 4.Multiply and remove common factors

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In the following exercise, divide. 8a2+16aa-4.a2+2a-24a2+7a+10÷2a2-6aa+5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite as the product of first times the reciprocal of the second.

Step 3. Factorize the denominator and numerator

Step 4.Multiply and remove common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Pure Maths

Decision Maths

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercise, divide.
$\frac{8 a^{2} + 16 a}{a - 4} . \frac{a^{2} + 2 a - 24}{a^{2} + 7 a + 10} \div \frac{2 a^{2} - 6 a}{a + 5}$