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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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Notes Over 9.5 Adding with Unlike Denominators Perform the indicated operation and simplify. The LCD contains each factor the greatest number of times.

Notes Over 9.5 Adding with Unlike Denominators Perform the indicated operation and simplify. The LCD contains each factor the greatest number of times.

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