Multiplying and Dividing Rational Expressions

Explore multiplication, division and reciprocals, checking a product.

Lesson 2 of 53 parts Practice Flashcards

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Multiplication

Objective: Explain multiplication and use it to solve or interpret a problem.

Multiply numerators and denominators, factor, and cancel common nonzero factors; list restrictions from every original denominator. All inputs excluded by the original denominators.

Worked examples

Try itMultiplying and Dividing Rational Expressions — practice 1.1: At x=5, evaluate (x/2)·(2/6).Show answer

Step 1: Cancel the nonzero factor 2. Step 2: The product becomes x/6. Step 3: At x=5, it is 5/6.

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Multiplication

Objective: Explain multiplication and use it to solve or interpret a problem.

Multiply numerators and denominators, factor, and cancel common nonzero factors; list restrictions from every original denominator. All inputs excluded by the original denominators.

Worked examples

Try itMultiplying and Dividing Rational Expressions — practice 1.1: At x=5, evaluate (x/2)·(2/6).Show answer

Step 1: Cancel the nonzero factor 2. Step 2: The product becomes x/6. Step 3: At x=5, it is 5/6.

Division and Reciprocals

Objective: Explain division and reciprocals and use it to solve or interpret a problem.

Dividing by a rational expression means multiplying by its reciprocal; the divisor also cannot equal zero. Track both original denominator restrictions and divisor-zero restrictions. Division by zero is undefined.

Worked examples

Try itMultiplying and Dividing Rational Expressions — practice 2.1: At x=8, evaluate (x/3)÷(7/3).Show answer

Step 1: Multiply by the reciprocal: (x/3)·(3/7). Step 2: Cancel 3. Step 3: At x=8, the value is 8/7.

Checking a Product

Objective: Explain checking a product and use it to solve or interpret a problem.

Substitute an allowed input into the original and simplified forms to check numerical agreement; a few checks do not prove algebraic equivalence but catch errors. No, also justify the factor algebra.

Worked examples

Try itMultiplying and Dividing Rational Expressions — practice 3.1: At x=11, evaluate (x/4)·(4/3).Show answer

Step 1: Cancel the nonzero factor 4. Step 2: The product becomes x/3. Step 3: At x=11, it is 11/3.

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