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Rational Expressions

Chapter 12. Rational Expressions. Simplifying Rational Expressions. 5.1. Rational Expression. A rational expression is an expression that can be written in the form where P and Q are both polynomials and Q ≠ 0. Examples of Rational Expressions. Evaluating Rational Expressions.

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Rational Expressions

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  1. Chapter 12 Rational Expressions

  2. Simplifying Rational Expressions 5.1

  3. Rational Expression A rational expression is an expression that can be written in the form where P and Q are both polynomials and Q≠ 0. Examples of Rational Expressions

  4. Evaluating Rational Expressions To evaluate a rational expression for a particular value(s), substitute the replacement value(s) into the rational expression and simplify the result. Example Evaluate the following expression for y = 2.

  5. Evaluating Rational Expressions In the previous example, what would happen if we tried to evaluate the rational expression for y = 5? Since division by 0 is undefined, this expression is undefined when y = 5.

  6. Undefined Rational Expressions To find values for which a rational expression is undefined, find values for which the denominator is 0.

  7. Undefined Rational Expressions Find any values that make the following rational expression undefined. Example The expression is undefined when 15x + 45 = 0. So, the expression is undefined when x = 3.

  8. Simplifying Rational Expressions Simplifying a rational expression means writing it in lowest terms or simplest form. To do this, we need to use the Fundamental Principle of Rational Expressions If P, Q, and R are polynomials, and Q and R are not 0,

  9. Simplifying Rational Expressions To Simplify a Rational Expression Step 1: Completely factor the numerator and denominator. Step 2: Divide out factors common to the numerator and denominator. (This is the same as “removing a factor of 1.”)

  10. Helpful Hint When simplifying a rational expression, we look for common factors, not common terms.

  11. Simplifying Rational Expressions Example x2 + 5x 7x + 35 Simplify:

  12. Simplifying Rational Expressions Example Simplify: x2 + 3x – 4 x2 – x – 20

  13. Simplifying Rational Expressions Example Simplify: 7 – y y – 7

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