Download Chapter 6.1(a) Rational Functions and Multiplying and Dividing

Chapter 6.1(a) Rational Functions and Multiplying and Dividing Rational Expressions.notebook
February 20, 2017
Bellwork:
1) Write the equation and graph the line that contains the points (5, 6) and (9, ­2).
Chapter 6.1(a) Rational Functions and Multiplying and Dividing Rational Expressions
Factor: 2
2) 2x ­ 32x + 78
Be able to find the domain of a rational expression and Simplify a rational expression.
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3) 3x + 2x ­ 16
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Finding the domain of rational expressions.
Rational Number (fraction): Is a number that can be written as the quotient of two integers p and q as long as q is not zero.
Rational Expression: is an expression that can be written as the quotient of two polynomials P and Q as long as Q is not 0.
examples:
Domain: all the possible input values (x­values).
As with fractions, a rational expression is undefined if the denominator is 0.
If a variable is replaced with a number that makes the denominator 0, we say the rational expression is undefined for this value of the variable.
Example: The expression Rational Function: rational expressions are sometimes used to describe functions. is undefined when x = ­1,
because replacing x with ­1 results in a denominator of 0. The domain of is then:
{x x is a real number and x ≠ ­1}
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Feb 9­7:56 AM
1) Find the domain of each rational function.
2) Find the domain of each rational function.
Domain is all real numbers except for values that make the denominator zero.
a. a. b.
b.
If possible, factor the denominator 1st
c.
c.
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Chapter 6.1(a) Rational Functions and Multiplying and Dividing Rational Expressions.notebook
February 20, 2017
To simplify a rational expression (write it in lowest terms), is similar to the method we use to simplify fractions.
We will use the same method to simplify rational expressions.
To simplify we need to "remove factors of 1".
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Example: =
=
=
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Feb 11­4:02 PM
4) Simplify:
a.
Simplify or Writing a Rational Expression in Lowest Terms:
b.
Step 1: Completely factor the numerator and denominator of the rational expression.
Step 2: Divide out factors common to the numerator and denominator. ("removing a factor of 1")
3) Simplify each rational expression.
c.
a. d. b. Feb 11­4:02 PM
Feb 11­4:03 PM
Homework
Simplifying Rational Expressions WS
Feb 9­9:21 AM
Feb 11­10:50 AM
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