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**Complex Rational Expressions**

Section 6.4

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**What is a complex fraction?**

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction. Some examples of complex fractions are: and

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**Method I: Simplifying a Complex Fraction**

Step 1: If needed, rewrite the numerator and denominator so that they are each a single fraction. * Combine all the parts of the numerator to form one fraction and all of the parts of the denominator to form another fraction. Step 2: Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator. Step 3: If needed, simplify the rational expression.

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Example 1: Step 1: Rewrite the numerator and denominator so that they are each a single fraction. TOP BOTTOM

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Example 2: Rewrite fractions with LCD of ab.

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**Method II: Simplifying a Complex Fraction**

Step 1: Multiply the numerator and denominator of the overall complex fractions by the LCD of the smaller fractions. Recall that when you multiply the exact same thing to the numerator and the denominator, the result is an equivalent fraction. Step 2: If needed, simplify the rational expression.

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Example 3: Step 1: Multiply the numerator and denominator by the LCD of the smaller fractions.

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**Step 2. Simplify the rational expression.**

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Example: What is the LCD of a, b, and ab2?

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Example:

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Example:

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Example:

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EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.

EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.

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