Algebra 1: Concepts and Skills

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Chapter 11 : Rational Equations and Functions
11.5 Adding and Subtracting with Like Denominators

#### 11.5 Problem Solving Help

Help for Exercises 34-39 on page 661

In Exercises 34-37, as with numerical fractions, addition and subtraction of fractions which include rational expressions can only be performed when the fractions have a common denominator. If the fractions have a common denominator, the next step is to add or subtract numerators, keeping the denominator the same. Be careful if you are subtracting expressions with more than one term in the numerator. The following example illustrates a common mistake made with this type of situation.

Simplify  .

To avoid this type of mistake, it is a good idea to place parentheses around the entire numerator of expressions that contain more than one term, especially if subtraction is being performed.

In Exercise 38, you are multiplying two factors in the form a(b+ c). Use the distributive property to rewrite this expression in the form ab+ ac. Look for common factors than can be divided out from the resulting rational expressions.

The expression in Exercise 39 is of the form (b+ c) ÷ a, which can be rewritten using multiplication as . Then apply the distributive property to rewrite the expression in the form . Look for common factors only after this step is complete.