/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 8.105 Simplify:聽b-3bb+52b+5+1b-5... [FREE SOLUTION] | 91影视

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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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