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Math 025 Unit 5 Section 6.4

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Objective: To simplify a complex fraction A complex fraction is a fraction whose numerator or denominator contains one or more fractions. 1 – 4x24x2 1 + 2x2x To simplify: 1. Find the LCD of all the fractions 2. Multiply the numerator and denominator by that LCD 3. Simplify the resulting fraction

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1 – 4x24x2 1 + 2x2x Objective: To simplify a complex fraction The LCM for x and x 2 is x 2 x2x2 x2x2 = x 2 – 4 (x – 2)(x + 2) x(x + 2) = = x – 2 x 1 1 x 2 + 2x

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1x1x 1212 1x21x2 1414 Objective: To simplify a complex fraction The LCM for x, x 2, 2 and 4 is 4x 2 4x 2 = 4x + 2x 2 2x(2 + x) (2 – x)(2 + x) = = 2x 2 – x 1 1 + – 4 – x 2

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1 – – 2x2x 1 – + 11 Objective: To simplify a complex fraction The LCM for x and x 2 is x 2 x2x2 x2x2 = x 2 – 2x – 15 x 2 – 11x + 30 (x – 5)(x + 3) (x – 6)(x – 5) = = x + 3 x – 6 1 1 15 x 2 30 x 2 x

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x – 8 + x – + Objective: To simplify a complex fraction The LCD is (x + 4) (x + 4) x 2 + 4x – 8x – 32 + 20 x 2 + 4x – 10x – 40 + 24 = = x – 6 x – 8 20 x + 4 10 24 x + 4 (x + 4) = x 2 – 4x – 12 x 2 – 6x – 16 = (x – 6)(x + 2) (x – 8)(x + 2)

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