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simplifying rational algebraic expressions

Mr. Dave Clausen. 2. State Standard

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simplifying rational algebraic expressions

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    1. SimplifyingRational Algebraic Expressions By Mr. Dave Clausen La Cańada High School

    2. Mr. Dave Clausen 2

    3. Mr. Dave Clausen 3 Rational Numbers Remember that a rational number is any number that can be written as a ratio:

    4. Mr. Dave Clausen 4 Algebraic Expressions Recall that an algebraic expression is: a number a variable a sum, difference, or product that contains one or more variables. For example: y2 - 2y + 6, 2c2d, x, -3, etc.

    5. Mr. Dave Clausen 5 Rational Algebraic Expression Therefore, a rational algebraic expression or rational expression is: a quotient of polynomials. Remember that a ? b is the same as which is also the same as ab-1 Don’t forget that a negative exponent tells us to take the reciprocal of the number or variable. Also remember that the negative exponent only applies to the variable “b” and not to the variable “a” in the example above.

    6. Mr. Dave Clausen 6 Examples: Here are some examples of rational algebraic expressions:

    7. Mr. Dave Clausen 7 Simplification Rule Reminder: Simplification of Rational Expressions If a, b, and r are real numbers with b ? 0 and r ? 0, then

    8. Mr. Dave Clausen 8 Simplifying Rational Algebraic Expressions Simplifying a rational algebraic expression is very similar to simplifying a rational number (fraction) Find the GCF of the numerator and denominator and divide both by the GCF A fraction is fully simplified when the GCF is 1 (one). In other words: factor the numerator and denominator completely. Any factor divided by itself simplifies (reduces) to 1.

    9. Mr. Dave Clausen 9 Strategy for Simplifying Rational Algebraic Expressions To simplify rational algebraic expressions: 1) Factor the numerator completely. 2) Factor the denominator completely. 3) Simplify (reduce) any like FACTORS (not terms).

    10. Mr. Dave Clausen 10 “Funny” Math “Funny” Math

    11. Mr. Dave Clausen 11 Example 1

    12. Mr. Dave Clausen 12 Example 2

    13. Mr. Dave Clausen 13

    14. Mr. Dave Clausen 14 Example 4

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