Chapter 11: Q11. (page 735)

Simplify the complex fraction. Show your work.
$\frac{\frac{5}{x - 3}}{\frac{x - 6}{x^{2} - x - 6}}$

Short Answer

Expert verified

The simplified complex fraction is $\frac{5 (x + 2)}{x - 6}$ .

Step by step solution

Step 1. State the concept of complex fractions.

In a complex fraction, $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a d}{b c}$ , wherein there are one or more fractions in the numerator and denominator where role="math" localid="1648022780063" $a, b, c,$ and $d$ can be numbers or polynomials.

Step 2. Simplify the expression by multiplying with the reciprocal.

First, multiply the numerator with the reciprocal of the denominator and then further simplify.

$\frac{\frac{5}{x - 3}}{\frac{x - 6}{x^{2} - x - 6}} = \frac{5}{x - 3} \div \frac{x - 6}{x^{2} - x - 6} = \frac{5}{x - 3} \times \frac{x^{2} - x - 6}{x - 6}$

Step 3. Simplify the expression.

To further simplify factor $x^{2} - x - 6$ and cancel out the common terms.

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Simplify the complex fraction. Show your work.
$\frac{\frac{5}{x - 3}}{\frac{x - 6}{x^{2} - x - 6}}$

Short Answer

Step by step solution

Step 1. State the concept of complex fractions.

Step 2. Simplify the expression by multiplying with the reciprocal.

Step 3. Simplify the expression.

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Simplify the complex fraction. Show your work.5x−3x−6x2−x−6

Short Answer

Step by step solution

Step 1. State the concept of complex fractions.

Step 2. Simplify the expression by multiplying with the reciprocal.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify the complex fraction. Show your work.
$\frac{\frac{5}{x - 3}}{\frac{x - 6}{x^{2} - x - 6}}$