1. Simplifying Rational Expressions
7.1
Simplifying Rational Expressions
1. Evaluate rational expressions.
2. Find numbers that cause a rational expression to be undefined.
3. Simplify rational expressions containing only monomials.
4. Simplify rational expressions containing multiterm polynomials.

2. Rational expression: An expression that can be
written in the form , where P and Q are
polynomials and Q 0.
Examples:
Rational = Fraction

3. Evaluate:

4. Evaluate:
Undefined
In working with rational expressions, we must be conscious of values that make the denominator equal 0.

5. The expression is undefined when x is 5.
When will this expression be undefined?
When will the denominator equal 0?
Set the denominator = 0 and solve.
It’s OK for the numerator to = 0.
The expression is undefined when x is 5.

6. The expression is undefined when x is 5 or 2.
When will this expression be undefined?
When will the denominator equal 0?
Set the denominator = 0 and solve.
The expression is undefined when x is 5 or 2.

7. The expression is undefined when p is 0 or -6.
When will this expression be undefined?
The expression is undefined when p is 0 or -6.

8. We can reduce common FACTORS.
NEVER reduce terms!

9. Simplify:
Factors or terms?
Reduce common factors.

10. Simplify:
Factors or terms?
Reduce common factors.

11. Simplify:
Factors or terms?
Reduce common factors.

12. Simplify:
Factors or terms?
Reduce common factors.

13. Simplify: 2 1

14. Simplify:
Factor out -1 to reverse the order of the terms.
-2(x - 3)

15. Copyright © 2011 Pearson Education, Inc.
Simplify.
a) 5 b) c) d)
Copyright © 2011 Pearson Education, Inc.
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16. Copyright © 2011 Pearson Education, Inc.
Simplify.
a) 5 b) c) d)
Copyright © 2011 Pearson Education, Inc.
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17. Copyright © 2011 Pearson Education, Inc.
Simplify.
a) –10x b) c) d)
Copyright © 2011 Pearson Education, Inc.
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18. Copyright © 2011 Pearson Education, Inc.
Simplify.
a) –10x b) c) d)
Copyright © 2011 Pearson Education, Inc.
7.1