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.

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

Evaluate:

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

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.

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.

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.

We can reduce common FACTORS. NEVER reduce terms!

Simplify: Factors or terms? Reduce common factors.

Simplify: Factors or terms? Reduce common factors.

Simplify: Factors or terms? Reduce common factors.

Simplify: Factors or terms? Reduce common factors.

Simplify: 2 1

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

Copyright © 2011 Pearson Education, Inc. Simplify. a) 5 b) c) d) Copyright © 2011 Pearson Education, Inc. 7.1

Copyright © 2011 Pearson Education, Inc. Simplify. a) 5 b) c) d) Copyright © 2011 Pearson Education, Inc. 7.1

Copyright © 2011 Pearson Education, Inc. Simplify. a) –10x b) c) d) Copyright © 2011 Pearson Education, Inc. 7.1

Copyright © 2011 Pearson Education, Inc. Simplify. a) –10x b) c) d) Copyright © 2011 Pearson Education, Inc. 7.1