# 10.1 Simplifying Rational Expressions - PowerPoint PPT Presentation

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10.1 Simplifying Rational Expressions. Goal : to simplify a rational expression. Simplifying Rational Expressions. A “ ratio nal expression ” is the quotient of two polynomials. (division). Simplifying Rational Expressions.

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10.1 Simplifying Rational Expressions

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### 10.1 Simplifying Rational Expressions

• Goal: to simplify a rational expression

### Simplifying Rational Expressions

• A “rational expression” is the quotient of two polynomials. (division)

### Simplifying Rational Expressions

• A “rational expression” is the quotient of two polynomials. (division)

• A rational expression is in simplest form when the numerator and denominator have no common factors (other than 1)

### Simplifying Rational Expressions

• A “rational expression” is the quotient of two polynomials. (division)

• A rational expression is in simplest Form when the numerator and denominator have no common factors (other than 1)

### How to get a rational expression in simplest form…

• Factor the numerator completely (factor out a common factor, difference of 2 squares, bottoms up)

• Factor the denominator completely (factor out a common factor, difference of 2 squares, bottoms up)

• Cancel out any common factors (not addends)

### Difference between a factor and an addend

• A factor is in between a multiplication sign

Example:

x + 33x + 9

x – 9 6x + 3

Factor

a-b = -1

b-a