Intermediate Algebra chapter 7

Complex Fractions
Chapter 7

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What is a Complex Fraction?

A complex fraction is a rational expression whose numerator and denominator are themselves rational expressions.

Since the numerator and denominator of the complex fraction are fractions themselves, the numerator and denominator are each called secondary fractions.

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Simplifying Complex Fractions

The steps for 2 methods of simplifying complex fractions are given here.

Method 1:  Multiplying by a Common Denominator

1. Find the lowest common denominator of the two secondary fractions.
2. Multiply both the numerator and denominator of the complex fraction by this lowest common denominator.
3. Simplify (reduce to lowest terms) the resulting rational expression.

Method 2:  Simplifying Numerator and Denominator

1. Simplify (reduce to lowest terms) each secondary fraction.

Solving Rational Equations

What is a Rational Equation? A rational equation is an equation that contains at least one rational expression. To Solve a Rational Equation...... Determine the lowest common denominator of all rational expressions in the equation. Multiply both sides of the equation by the lowest common denominator. Simplify by removing parentheses and combining like terms. Solve the equation resulting from step 4. Check the solution in the original equation. This step is essential since it is here that you will eliminate extraneous solutions (see below). What are Extraneous Solutions? An extraneous solution is a value that you think is a solution because it was found by the solving process but, this value does not solve the original equation. The way that you determine that a value is an extraneous solution is by checking that value in the original equation: If a value that you think is a solution does not solve the original equation, then that value is an extraneous solution. The check step is where extraneous solutions are found. Always check all solutions in the original equation to make sure they solve the originalequation.

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