Simplifying Rational Algebraic Expressions

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SimplifyingRational Algebraic Expressions

• By
• Mr. Dave Clausen
• La Cañada High School

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State Standard Objectives

• Algebra 2 Standard 7.0 Students add, subtract,
  multiply, divide, reduce, and evaluate rational
  expressions with monomial and polynomial
  denominators and simplify complicated rational
  expressions, including those with negative
  exponents in the denominator.
• Objective 1 To understand what a rational
  algebraic expression is.
• Objective 2 To simplify rational algebraic
  expressions.
• Objective 3 To find the domain and zeros of a
  rational function.

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Rational Numbers

• Remember that a rational number is any number
  that can be written as a ratio

where a and b are integers and b ? 0.
For example -98, 6, 325, 9.6, -4.1, 0, and
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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.

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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
• Dont 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.

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Examples

• Here are some examples of rational algebraic
  expressions

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Simplification Rule

• Reminder Simplification of Rational Expressions
• If a, b, and r are real numbers with b ? 0 and r
  ? 0, then

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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.

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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).

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Funny Math

• Funny Math

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Example 1
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Example 2
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Example 3
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Example 4

1. Find the Domain of the Rational Function.
2. Find the zeros of the Rational Function, if there
   are any.