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Simplifying Rational Expressions
Multiplying and Dividing Rational ExpressionsRemember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.
Remember, denominators can not = 0.Now,lets go through the steps to simplify a rational expression.
Step 1: Factor the numerator and the denominator completely looking for common factors.Next
What is the common factor?Step 2: Divide the numerator and denominator by the common factor.
Step 3: Multiply to get your answer.1 Step 3: Multiply to get your answer.
Looking at the answer from the previous example, what value of x would make the denominator 0?The expression is undefined when the values make the denominator equal to 0
How do I find the values that make an expression undefined?Completely factor the original denominator.
Factor the denominatorThe expression is undefined when: a= 0, 2, and -2 and b= 0.
Lets go through another example.Factor out the GCF Next
Now try to do some on your own.Also find the values that make each expression undefined?
Remember how to multiply fractions:First you multiply the numerators then multiply the denominators.
The same method can be used to multiply rational expressions.1
Step #1: Factor the numerator and the denominator.Let’s do another one. Step #1: Factor the numerator and the denominator. Next
Step #2: Divide the numerator and denominator by the common factors.1
Step #3: Multiply the numerator and the denominator.Remember how to divide fractions?
Multiply by the reciprocal of the divisor.1 5 4
Dividing rational expressions uses the same procedure.Ex: Simplify
Now you try to simplify the expression:
Now try these on your own.
Here are the answers:
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