Rational Expressions Simplifying Algebra B

Simplifying Rational Expressions The objective is to be able to simplify a rational expression

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.

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

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.

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

Factoring the Numerator and Denominator Factor the numerator. Factor the denominator. Divide out the common factors. Write in simplified form.

Factoring Step 1: Factor the numerator and denominator

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

You Try It Simplify the following rational expressions.

Problem 1 Factor the numerator and denominator Divide out the common factors. Write in simplified form.

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.

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.

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.

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.

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.

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

Problem 1 Solution y  0 z  0

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

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

HW Pg. 463 #2 to 30 even