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	Roots - Radicals 1
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	Writing Linear Equations Using Slope and Point
	Factoring Trinomials with Leading Coefficient 1
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	Simplifying Expressions with Negative Exponents
	Solving Equations 3
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	Power of a Quotient Property of Exponents
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	Solving Linear Systems of Equations by Elimination
	The Quadratic Formula
	Fractions and Mixed Numbers
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	Factoring by Grouping
	Polar Form of a Complex Number
	Solving Quadratic Equations
	Simplifying Complex Fractions
	Algebra
	Common Logs
	Operations on Signed Numbers
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	Dividing Polynomials
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	Higher Degrees and Variable Exponents
	Solving Quadratic Inequalities with a Sign Graph
	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
	Solving Linear Equations
	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
	fractions
	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
	Straight Lines
	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
	Operations on Radicals
	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Simplifying Complex Fractions

A complex fraction is a fraction that contains other fractions.

Here are three examples of complex fractions.

There are two methods for simplifying complex fractions.

Procedure

To Simplify a Complex Fraction

Step 1 Write the numerator and denominator each as a single fraction.

Step 2 Rewrite the complex fraction using the division symbol, Ã·.

Step 3 Invert the second fraction and change Ã· to Â·.

Step 4 Multiply.

Example

Simplify:

Solution
Step 1 Write the numerator and denominator each as a single fraction. The numerator and denominator are already single fractions.
Step 2 Rewrite the fraction using Ã·.
Step 3 Invert the second fraction and change Ã· to Â·.
Step 4 Multiply.
Factor the numerators and denominators.
Cancel all pairs of common factors.
Multiply.
So, the result is .

Note

In , the numerator is and the denominator is .