 # Simplifying Rational Expressions.

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Simplifying Rational Expressions

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.

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 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

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

1 Next

Now you try to simplify the expression:

Now try these on your own.