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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 cannot = 0.

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## Simplifying

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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 cannot = 0.**Now, let’s go through the steps to simplifya rational expression.**Step 1: Factor the numerator and the denominator completely**looking for common factors: Numerator: Denominator:**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) makes the denom=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??**5x³ + 10x² = 5x²(x + 2)**• x³ - 6x² - 16x x(x² - 6x – 16) • = 5x²(x + 2) • x(x – 8)(x + 2) • Cancel out both (x + 2)’s • = 5x² = 5x • x(x – 8) (x – 8) • x² - 5x + 6 = (x – 2)(x – 3) • x² - 9 (x + 3)(x – 3) • Cancel out both (x – 3)’s • = (x – 2) • (x + 3)**Do you remember how to multiply fractions??**First you multiply the numerators then multiply the denominators.**1**1 1 1 1 1 1 1 1 The same method can be used to multiply rational expressions.**Let’s do another one.**Step #1: Factor the numerator and the denominator. Next**1**1 1 1 1 1 Step #2: Divide the numerator and denominator by the common factors.**Step #3: Multiply the numerator and the denominator.**Remember how to divide fractions?**1**5 1 4 Multiply by the reciprocal of the divisor.**Dividing rational expressions uses the same procedure.**Ex: Simplify**1**1 1 1 Next…**Now wasn’t that fun???!!!**Your homework is:

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