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6.4 Complex Fractions

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Complex Fractions A complex fraction is a fraction that has a fraction in its numerator or its denominator or both. Examples:

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**Simplifying Complex Fractions**

Method 1: Simplify the fraction by doing the operation indicated, then simplify. Method 2: Eliminate the smaller fractions by multiplying both numerator and denominator by the LCD of the entire fraction.

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Example 1 – Method 1 Division was the initial operation indicated. To perform this division, remember to multiply the numerator by the reciprocal of the denominator and then reduce.

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Example 1 – Method 2 The LCD for the entire fraction is n3 because we are looking at n and n3. After you multiply both numerator and denominator by this LCD, just reduce.

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Example 2 – Method 1 Do the operation indicated and subtract the two terms in the numerator. Then rewrite the division as a multiplication problem and simplify.

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Example 2 – Method 2 Multiply both numerator and denominator by LCD of the entire fraction ( t ) and then simplify.

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Example 3 – Method 1

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**Explanation of Example 3 – Method 1**

Do the addition and subtraction indicated in the numerator and denominator. Then rewrite the division in the form of multiplication. Factor and reduce if possible.

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Example 3 – Method 2

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**Explanation of Example 3 – Method 2**

Multiply both numerator and denominator by LCD of entire fraction. Then factor and simplify if possible.

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Other instructions Unless specified, you may use either Method 1 or 2, whichever one you prefer. Please look at all of the examples in the book. Please do assignment 6D for homework.

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6-3: Complex Rational Expressions complex rational expression (fraction) – contains a fraction in its numerator, denominator, or both.

6-3: Complex Rational Expressions complex rational expression (fraction) – contains a fraction in its numerator, denominator, or both.

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