Rational Expressions. Martin-Gay, Developmental Mathematics 2 Rational Expressions Examples of Rational Expressions.

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Presentation transcript:

Rational Expressions

Martin-Gay, Developmental Mathematics 2 Rational Expressions Examples of Rational Expressions

Martin-Gay, Developmental Mathematics 3 To evaluate a rational expression for a particular value(s), substitute the replacement value(s) into the rational expression and simplify the result. Evaluating Rational Expressions Example Evaluate the following expression for y =  2.

Martin-Gay, Developmental Mathematics 4 In the previous example, what would happen if we tried to evaluate the rational expression for y = 5? This expression is undefined! Evaluating Rational Expressions

Martin-Gay, Developmental Mathematics 5 We have to be able to determine when a rational expression is undefined. A rational expression is undefined when the denominator is equal to zero. The numerator being equal to zero is okay (the rational expression simply equals zero). Undefined Rational Expressions

Martin-Gay, Developmental Mathematics 6 Find any real numbers that make the following rational expression undefined. The expression is undefined when 15x + 45 = 0. So the expression is undefined when x =  3. Undefined Rational Expressions Example

Simplifying Rational Expressions

Martin-Gay, Developmental Mathematics 8 Simplifying a rational expression means writing it in lowest terms or simplest form. If P, Q, and R are polynomials, and Q and R are not 0, Simplifying Rational Expressions

Martin-Gay, Developmental Mathematics 9 Simplifying Rational Expressions  A “ ratio nal expression” is the quotient of two polynomials. (division)

Martin-Gay, Developmental Mathematics 10 Simplifying Rational Expressions  A rational expression is in simplest form when the numerator and denominator have no common factors (other than 1)

Martin-Gay, Developmental Mathematics 11 Simplifying Rational Expressions

Martin-Gay, Developmental Mathematics 12 How to get a rational expression in simplest form…  Factor the numerator completely (factor out a common factor)  Factor the denominator completely (factor out a common factor)  Cancel out any common factors ( not addends )

Martin-Gay, Developmental Mathematics 13 Difference between a factor and an addend  A factor is in between a multiplication sign  An addend is between an addition or subtraction sign  Example: x + 3 3x + 9 x – 9 6x + 3

Martin-Gay, Developmental Mathematics 14 Factor

Martin-Gay, Developmental Mathematics 15

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Martin-Gay, Developmental Mathematics 20 Wentz’s Shortcut

Martin-Gay, Developmental Mathematics 21 Opportunity for Mathematical Growth Please do your handout (17 questions)