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Simplifying Rational Expressions

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**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.

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**Remember, denominators can not = 0.**

Now,lets go through the steps to simplify a rational expression.

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**Step 1: Factor the numerator and the denominator completely looking for common factors.**

Next

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**What is the common factor?**

Step 2: Divide the numerator and denominator by the common factor.

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**Step 3: Multiply to get your answer.**

1 Step 3: Multiply to get your answer.

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**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

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**How do I find the values that make an expression undefined?**

Completely factor the original denominator.

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**Factor the denominator**

The expression is undefined when: a= 0, 2, and -2 and b= 0.

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**Lets go through another example.**

Factor out the GCF Next

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1 1

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**Now try to do some on your own.**

Also find the values that make each expression undefined?

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**Remember how to multiply fractions:**

First you multiply the numerators then multiply the denominators.

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**The same method can be used to multiply rational expressions.**

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**Step #1: Factor the numerator and the denominator.**

Let’s do another one. Step #1: Factor the numerator and the denominator. Next

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**Step #2: Divide the numerator and denominator by the common factors.**

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**Step #3: Multiply the numerator and the denominator.**

Remember how to divide fractions?

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**Multiply by the reciprocal of the divisor.**

1 5 4

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**Dividing rational expressions uses the same procedure.**

Ex: Simplify

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1 Next

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**Now you try to simplify the expression:**

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**Now try these on your own.**

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Here are the answers:

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