Chapter 7: Q. 7.48 (page 671)

Simplify the complex rational expression by writing it as division:
$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

Short Answer

Expert verified

The simplified answer is $\frac{1}{2 (x - 3)}$

Step by step solution

Step 1. Given information.

The following rational expression is given:

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

Step 2. Simplify the rational expression by division.

Rewrite the complex fraction as division:

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

Rewrite as the product of the first and the reciprocal of the second:

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

Now,

$x^{2} - 7 x + 12 = x^{2} - 4 x - 3 x + 12 x^{2} - 7 x + 12 = x (x - 4) - 3 (x - 4) x^{2} - 7 x + 12 = (x - 4) (x - 3)$

Factor:

$\frac{1}{(x - 3) (x - 4)} . \frac{x - 4}{2}$

Multiply:

$\frac{(x - 4)}{2 (x - 3) (x - 4)}$

Remove common factors from the numerator and the denominator:

$\frac{1}{2 (x - 3)}$

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Simplify the complex rational expression by writing it as division:
$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the rational expression by division.

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Simplify the complex rational expression by writing it as division:1x2-7x+122x-4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the rational expression by division.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Applied Mathematics

Mechanics Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by writing it as division:
$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$