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	Adding and Subtracting Rational Expressions With Unlike Denominators
	Multiplication by 25
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	Solving Quadratic Equations by Completing the Square
	Quotient Rule for Exponents
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	Independent, Inconsistent, and Dependent Systems of Equations
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	Powers of Ten
	Zero Power Property of Exponents
	The Vertex of a Parabola
	Rationalizing the Denominator
	Test for Factorability for Quadratic Trinomials
	Trinomial Squares
	Solving Two-Step Equations
	Solving Linear Equations Containing Fractions
	Multiplying by 125
	Exponent Properties
	Multiplying Fractions
	Adding and Subtracting Rational Expressions With the Same Denominator
	Quadratic Expressions - Completing Squares
	Adding and Subtracting Mixed Numbers with Different Denominators
	Solving a Formula for a Given Variable
	Factoring Trinomials
	Multiplying and Dividing Fractions
	Multiplying and Dividing Complex Numbers in Polar Form
	Power Equations and their Graphs
	Solving Linear Systems of Equations by Substitution
	Solving Polynomial Equations by Factoring
	Laws of Exponents
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	Systems of Linear Equations
	Properties of Rational Exponents
	Power of a Product and Power of a Quotient
	Factoring Differences of Perfect Squares
	Dividing Fractions
	Factoring a Polynomial by Finding the GCF
	Graphing Linear Equations
	Steps in Factoring
	Multiplication Property of Exponents
	Solving Systems of Linear Equations in Three Variables
	Solving Exponential Equations
	Finding the GCF of a Set of Monomials

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Simplifying Complex Fractions That Contain Addition or Subtraction

You have already simplified some complex fractions. Now we will learn how to simplify a complex fraction that contains addition or subtraction.

One way to begin is to carry out the addition or subtraction.

Procedure â€” To Simplify a Complex Fraction That Contains Addition or Subtraction.

Step 1 Perform any addition or subtraction.

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

Step 3 Invert the second fraction and change the division symbol, Ã·, to the multiplication symbol, Â·.

Step 4 Factor the numerators and denominators.

Step 5 Cancel all pairs of factors common to the numerators and denominators.

Step 6 Multiply the numerators. Multiply the denominators.

Example 1

Simplify:

Solution

Step 1 Perform any addition or subtraction.
In both the numerator and denominator the LCD of the fractions is wy. We write each fraction with LCD.
Then we add the fractions in the numerator and subtract the fractions in the denominator.
Step 2 Rewrite the complex fraction using a division symbol, Ã·.
Step 3 Invert the second fraction and change the division symbol, Ã·, to the multiplication symbol, Â·.
Step 4 Factor the numerators and denominators.
Step 5 Cancel all pairs of factors common to the numerators and denominators.
The common factors are 2, w, and y.
Step 6 Multiply the numerators. Multiply the denominators.

Thus,