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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 8.105 (page 960)

Simplify: $\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{(b^{2} + 2 b) (b - 5)}{3 b - 5}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}}$

02

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B} 梅 \frac{C}{D} = \frac{A}{B} 路 \frac{D}{C}$

03

Step 3. Rewrite the expression and then simplify.

Simplify and rewrite the complex fraction as division.

$= \frac{\frac{b (b + 5) - 3 b}{b + 5}}{\frac{2 (b - 5) + (b + 5)}{(b + 5) (b - 5)}} = \frac{\frac{b^{2} + 5 b - 3 b}{b + 5}}{\frac{2 b - 10 + b + 5}{(b + 5) (b - 5)}} = \frac{\frac{b^{2} + 2 b}{b + 5}}{\frac{3 b - 5}{(b + 5) (b - 5)}} = \frac{b^{2} + 2 b}{b + 5} 梅 \frac{3 b - 5}{(b + 5) (b - 5)}$

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

$= \frac{b^{2} + 2 b}{b + 5} 路 \frac{(b + 5) (b - 5)}{3 b - 5} = \frac{(b^{2} + 2 b) (b - 5)}{3 b - 5}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{(b^{2} + 2 b) (b - 5)}{3 b - 5}$ .

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Most popular questions from this chapter

Reese loves to drink healthy green smoothies. A 16 ounce serving of smoothie has 170 calories. Reese drinks 24 ounces of these smoothies in one day. How many calories of smoothie is he consuming in one day?

In the following exercises, simplify.

$\frac{15 x y}{3 x^{3} y^{3}}$

Ironing Lenore can do the ironing for her family鈥檚 business in h hours. Her daughter would take h + 2 hours to get the ironing done. If Lenore and her daughter work together, using 2 irons, the number of hours it would take them to do all the ironing is $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .

Simplify the complex fraction $\frac{1}{\frac{1}{h} + \frac{1}{h + 2}}$ .
Find the number of hours it would take Lenore and her daughter, working together, to get the ironing done if $h = 4$ .

Solve :

$1 - \frac{2}{a} = \frac{15}{a^{2}}$

In the following exercises, simplify.

$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

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