Simplifying Rational Expressions
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The document provides steps for dividing out common factors and factoring rational expressions: 1) Identify common factors in the numerator and denominator and divide them out. 2) Factor the numerator and denominator by identifying common factors in each expression. 3) Divide the factored numerator and denominator, simplifying the expression.
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Simplifying Rational Expressions
- 2. Divide out the common factors Factor the numerator and denominator and then divide the common factors
- 3. 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.
- 4. 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
- 5. Factoring the Numerator and Denominator Factor the numerator. Factor the denominator. Divide out the common factors. Write in simplified form.
- 6. Factoring Step 1 : Look for common factors to both terms in the numerator. 3 is a factor of both 3 and 9. X is a factor of both x 2 and x. Step 2 : Factor the numerator. 3 3 12 3 x x x ( )
- 7. Factoring Step 3 : Look for common factors to the terms in the denominator and factor. The denominator only has one term. The 12 and x 3 can be factored. The 12 can be factored into 3 x 4. The x 3 can be written as x • x 2 . 3 3 3 4 2 x x x x ( )
- 8. Divide and Simplify Step 4 : Divide out the common factors. In this case, the common factors divide to become 1. Step 5 : Write in simplified form. x x 3 4 2
- 9. You Try It Simplify the following rational expressions.