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Rational Expressions Simplifying Algebra B

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**Simplifying Rational Expressions**

The objective is to be able to simplify a rational expression

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**Vocabulary Polynomial – The sum or difference of monomials.**

Rational expression – A fraction whose numerator and denominator are polynomials. Reduced form – a rational expression in which the numerator and denominator have no factors in common.

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**Simplifying Rational Expressions**

Our aim is to cancel common factors Factor the numerator and denominator and then cancel the common factors We can cancel only factors NOT TERMS

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**Dividing Out Common Factors**

Step 1 – Identify any factors which are common to both the numerator and the denominator. The numerator and denominator have a common factor. The common factor is the five.

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**Dividing Out Common Factors**

Step 2 – Divide out the common factors. The fives can be divided since 5/5 = 1 The x remains in the numerator. The (x-7) remains in the denominator

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**Factoring the Numerator and Denominator**

Factor the numerator. Factor the denominator. Divide out the common factors. Write in simplified form.

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Factoring Step 1: Factor the numerator and denominator

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**Divide and Simplify x + 3 4 x 2**

Step 2: Divide out the common factors. In this case, the common factors divide to become 1. Step 5: Write in simplified form. x + 3 2 4 x

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You Try It Simplify the following rational expressions.

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**Problem 1 Factor the numerator and denominator**

Divide out the common factors. Write in simplified form.

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**Problem 2 Factor the numerator and denominator**

You Try It Problem 2 Factor the numerator and denominator Divide out the common factors. Write in simplified form.

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**Problem 3 Factor the numerator and denominator**

You Try It Problem 3 Factor the numerator and denominator Divide out the common factors. Write in simplified form.

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**Problem 4 Factor the numerator and denominator**

You Try It Problem 4 Factor the numerator and denominator Divide out the common factors. Write in simplified form.

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**Problem 5 Factor the numerator and denominator**

You Try It Problem 5 Factor the numerator and denominator Divide out the common factors. Write in simplified form.

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**Restrictions on Rational Expressions**

For what value of x is undefined? It is undefined for any value of “x” which makes the denominator zero. The restriction is that x cannot equal 5.

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YOU TRY IT What are the excluded values of the variables for the following rational expressions?

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Problem 1 Solution y 0 z 0

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**Problem 2 Solution 2x - 12 = 0 ANSWER 2x - 12 + 12 = 0 + 12 x 6**

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**Problem 3 Solution C2 + 2C - 8 = 0 Answer C 2 (C-2)(C+4) = 0 C -4**

C-2 = or C + 4 = 0 C-2+2 = C = 0 - 4 C = or C = -4 Answer C 2 C -4

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HW Pg. 463 #2 to 30 even

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