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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. 8.100 (page 957)

Simplify: $\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{1}{2 (x - 3)}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

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.

Rewrite the complex fraction as division.

$\frac{1}{x^{2} - 7 x + 12} 梅 \frac{2}{x - 4}$

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

$= \frac{1}{x^{2} - 7 x + 12} 路 \frac{x - 4}{2} = \frac{1}{x^{2} - 4 x - 3 x + 12} 路 \frac{x - 4}{2} = \frac{1}{x (x - 4) - 3 (x - 4)} 路 \frac{x - 4}{2} = \frac{1}{(x - 4) (x - 3)} 路 \frac{x - 4}{2} = \frac{1}{2 (x - 3)}$

04

Step 4. Conclusion.

The simplified form of the given expression is $\frac{1}{2 (x - 3)}$ .

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