Here the denominators are 5 and 10 so we can Method 2 for

Here the denominators are 5 and 10 so we can method 2

This preview shows page 28 - 37 out of 37 pages.

Here the denominators are 5 and 10, so we can write 28
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6.4: Method 2 for Simplifying Complex Fractions The second approach interprets the complex fraction as division and applies the earlier work in dividing fractions in which you invert and multiply . Recall that by the fundamental principle we can always multiply the numerator and denominator of a fraction by the same nonzero quantity. 29
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6.4.1: Use the Fundamental Principle to Simplify Complex Fractions Examples: Simplify the followings: 1. 2. 30
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6.4.2: Use division to simplify complex fractions Examples: Simplify the following: 1. 2. 31 2 6 5 4 18 3 2 2 2 x x x x x x
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6.4.2: Use division to simplify complex fractions The following algorithm summarizes our work with complex fractions. 32
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6.5: Solving Rational Equations Rational Equations Applications of algebra will often result in equations involving rational expressions. The objective in this section is to develop methods to find solutions for such equations. The usual technique for solving such equations is to multiply both sides of the equation by the least common denominator (LCD) of all the rational expressions appearing in the equation. The resulting equation will be cleared of fractions, and we can then proceed to solve the equation as before. 33
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6.5: Solving Rational Equations Examples: Solve the following rational equations: 1. 2. 3. 34
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6.5: Solving Rational Equations Examples: Solve the following rational equations: 1. 2. 3. 35
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6.5: Solving Rational Equations Examples: Solve the following rational equations: 1. 2. 36 1 6 6 1 3 3 3 1 2 x x x x x x 1 6 2 7 3 5 x x x
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6.5: Solving Rational Equations The following algorithm summarizes our work in solving equations containing rational expressions. 37
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