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Simplifying Rational Expressions: Homework and Classwork Guide

This guide focuses on the concept of simplifying rational expressions, a critical aspect of algebra. Students are required to copy homework assignments into their planners, complete exercises from the textbook, and engage with new concepts in class. Rational expressions are defined as expressions that can be expressed as a ratio of two polynomials where the denominator is not zero. Students will learn to identify excluded values, factor, and simplify expressions to their simplest form. Practice problems, including examples of rational numbers and excluded values, will enhance understanding.

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Simplifying Rational Expressions: Homework and Classwork Guide

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  1. Do Now 5/29/09 • Copy HW in your planner. • Text p. 797, #4-38 evens • Take out HW from last night. • Cumulative Test • In your notebook, define and give two examples of rational numbers. • Text p. 762, #1-16 all, not 2

  2. 1) 40 3) 2 4) -1 5) (x – 5)(x + 3) 6) 2(x – 3)(x – 1) 7) (3x + 5)(3x – 5) 8) 3x(x + 4)(x – 4) 9) 1 1/12 10) 19/40 11) 1/3 12) 1 1/4 13) 9/4 14) 6 15) -3, 2 16) 13 HomeworkText p. 762, #1-16 all; not 2

  3. Objective • SWBAT simplify rational expressions.

  4. Section 12.4 “Simplify Rational Expressions” • A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction) of two polynomials where the denominator is not 0. • A rational expression is UNDEFINEDwhen the denominator is equal to 0. • A number that makes a rational expression undefined is called an EXCLUDED VALUE.

  5. EXAMPLE 1 Find the excluded values, if any, of the expression. Use quadratic formula to find when w = 0. Factor There are no excluded values

  6. Simplify Rational Expressions • To simplify a rational expression, you can factor the numerator and denominator and then divide out any common factors. • A rational expression is in SIMPLEST FORMif the numerator and denominator have no factors in common other than 1.

  7. EXAMPLE 2 Simplify the rational expression, if possible. State the excluded values. Factor

  8. EXAMPLE 3 Simplify the rational expression, if possible. State the excluded values. Factor Factor

  9. EXAMPLE 4 Recognize opposites Simplify the rational expression, if possible. State the excluded values. Factor Recognize opposites Multiply by -1 Rewrite (4-x) as -(x-4) Factor Recognize opposites Multiply by -1 Rewrite (z-5) as -(z+5)

  10. Classwork/Homework • Text p. 797, #4-36 multiples of 4

  11. HomeworkPractice worksheet 12.4 evens 14) 2) 4) 16) 6) 18) 8) 10) 12)

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