Download Section 6.1 Rational Functions, and Multiplying and Dividing

MTH95 Module 3
Section 6.1 Rational Functions, and Multiplying and Dividing Rational Expressions
Fractions are rational numbers. Rational numbers have an integer in the numerator and an
integer in the denominator. We can simplify rational numbers by canceling common factors,
we can multiply and divide (fairly easy) and we can add and subtract (a little more work).
Rational functions have a polynomial in the numerator and a polynomial in the denominator.
We can simplify rational functions by factoring and canceling common factors, we can multiply
and divide, and we can add and subtract.
Finding the Domain of a Rational Expression
We will save graphing rational functions for College Algebra, but we should talk about domain.
A rational expression is undefined if the denominator is 0. The domain of a rational function
will be all real numbers except for those that make the denominator 0.
Examples:
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Simplifying Rational Expressions
In a nutshell: factor and cancel.
These have a trick:
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MTH95 Module 3
Multiplying Rational Expressions
Factor everything, multiply (but don’t multiply out), simplify by cancelling common factors
Examples:
Dividing Rational Expressions
Dividing by 2 is the same as multiplying by _____________
Dividing by is the same as multiplying by _____________
In a nutshell: Flip, factor everything, simplify
Examples:
Section 6.2: Adding and Subtracting Rational Expressions
Add or Subtract Rational Expressions with Common Denominators
As long as we are starting with common denominators, adding and subtracting is not bad at all.
Just be extra careful with subtracting.
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Identifying the LCD of Rational Expressions
Let’s start with a review of adding rational numbers (aka fractions)
Finding the LCD: Factor each denominator. The LCD is the product of each different factor,
raised to the highest number of times it appears in any one denominator.
Examples:
Adding/Subtracting Rational Expressions with unlike denominators
These have the potential to be looong problems.
Pencils sharp? Plenty of paper?
Step1: Factor the denominators and find the LCD
Step 2: Build up each rational expression to have the LCD as its denominator.
Step 3: Add or subtract the numerators and keep the common denominator.
Step 4: Simplify the result, if possible.
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MTH95 Module 3
Examples:
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