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How to Add and Subtract Rational Expressions with a Common Denominator
To add or subtract rational expressions that already share the same denominator, follow a three-step procedure:
Step 1. Add or subtract the numerators and place the result over the common denominator.
Step 2. Factor the numerator and denominator completely.
Step 3. Simplify by dividing out any common factors shared by the numerator and denominator.
This procedure parallels the approach used for numerical fractions with a common denominator, but introduces the essential additional requirement of factoring. Because the numerators and denominators are polynomials rather than plain numbers, the combined numerator may share common polynomial factors with the denominator. These shared factors must be uncovered through complete factoring and then canceled to express the result in its simplest form. Skipping the factoring step can leave the answer unsimplified even when common factors exist.
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A logistics analyst is combining two shipping rate formulas, represented as rational expressions, that share a common denominator. To ensure the final formula is in its simplest form, what is the correct sequence of steps they should follow?
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