Simplifying Multiplying and Dividing Rational Expressions Remember that
Simplifying
Multiplying and Dividing Rational Expressions Remember 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.
1 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? x= -1 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 denominator The expression is undefined when: a= 0, 2, and -2 and b= 0.
Lets go through another example. Factor out the GCF Next
1 1
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 1 1 1 1
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 1 1
Step #3: Multiply the numerator and the denominator. Remember how to divide fractions?
Multiply by the reciprocal of the divisor. 1 5 1 4
Dividing rational expressions uses the same procedure. Ex: Simplify
1 1 Next
Now you try to simplify the expression:
Now try these on your own.
Here are the answers:
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