Chapter 7: Q. 55 (page 653)

For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} \div \frac{5 m^{2} + 10 m}{2 m - 10}$

Short Answer

Expert verified

The simplified expression is $= \frac{4 (m + 8) (m + 7)}{3 (m - 4) (m + 2)}$

Step by step solution

Step 1. Given Information

$\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} \div \frac{5 m^{2} + 10 m}{2 m - 10}$

$= \frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} . \frac{2 m - 10}{5 m^{2} + 10 m}$

Step 2. Factor the numerator and denominator

$\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} . \frac{2 m - 10}{5 m^{2} + 10 m} = \frac{10 m (m + 8)}{3 (m - 3)} . \frac{(m + 7) (m - 3)}{(m - 4) (m - 5)} . \frac{2 (m - 5)}{5 m (m + 2)}$

Step 3. Multiply numerators and denominators

$= \frac{2 \times 10 m (m + 8) (m + 7) (m - 3) (m - 5)}{3 \times 5 m (m - 3) (m - 4) (m - 5) (m + 2)} .$

Step 4. Remove common factors and simplify

$= \frac{4 (m + 8) (m + 7)}{3 (m - 4) (m + 2)}$

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For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} \div \frac{5 m^{2} + 10 m}{2 m - 10}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the numerator and denominator

Step 3. Multiply numerators and denominators

Step 4. Remove common factors and simplify

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For the following exercises, perform the indicated operations.10m2+80m3m-9.m2+4m-21m2-9m+20÷5m2+10m2m-10

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the numerator and denominator

Step 3. Multiply numerators and denominators

Step 4. Remove common factors and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Discrete Mathematics

Calculus

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} \div \frac{5 m^{2} + 10 m}{2 m - 10}$