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# Calc section 0.5

## on Sep 21, 2011

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Rational expressions

Rational expressions

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## Calc section 0.5Presentation Transcript

• 0.5 Rational ExpressionsGoal: To Simplify and rationalize the denominator of rational expressions.
Rational Expression:
A rational expression is fraction whose numerator and denominator are polynomials
For example:
• Rational Functions:
• Let u(x) and v(x) be polynomial functions. The function
Is a rational function. The domain of this rational expression is the set of all real numbers for which v(x) ≠ 0.
• The key issue with the domain of rational expressions is that we can never divide by zero.
Recall: Dividing by zero is undefined
ex.
Domain = (-∞,0) U (0,∞)
• Example:
Domain = (-∞,3) U (3,7) U (7,∞)
Whenever we work with rational expressions, we have to make sure we check the domain. We never want to have an answer that results in the function becoming undefined.
• Find the domain
• (-∞,2) U (2, ∞)
Find the domain
• (-∞,1) U (1, ∞)
• To simplify rational expressions:
Factor both numerator and denominator
Find domain of denominator
Reduce where possible
• Example:
• (-∞, 3)U(3,7)U(7,∞) is the domain of the denominator
(-∞, 3)U(3,∞) We list this as our domain restriction since we have canceled the factor (x-3) on the graph there is a whole at x = 3
• Using your table, see what the value of y is when x = 3, what is different about x = 7?
*This will lead us to removable and non removable discontinuity in ch. 1
• Example: Simplify
(-∞, 0)U(0,1)U(1,∞) is the domain of the denominator
x Є(-∞, 0)U(0,1)U(1,∞)
• To Multiply/Divide rational expressions:
• Factor both numerator and denominator
• Find domain of denominator for both expressions (also denominator of reciprocal when you divide)
• Reduce where possible
• Example:
• x Є(-∞, -3) U(-3,2)U(2,3)U(3,∞)
x Є(-∞,2)U(2,3)U(3,∞)
• EX.
x Є(-∞, -1) U(-1,0)U(0,1)U(1,∞)
x Є(-∞, -6) U(-6, -1) U(-1,0)U(0,1)U(1,∞)