Write how the multiplying rational expressions and multiplying numerical fractions are similar and how they are different.
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Answer to Problem 8LC
Explanation of Solution
Given:
How are multiplying rational expressions and multiplying numerical fractions similar? How are they different?
Concept Used:
Just as you can multiply and divide fractions, you can multiply and divide rational expressions. A fraction is called that contains a polynomial as the numerator, denominator, or both.
In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions.
Example:
In practice it is easier to factor the numerators and denominators and "cancel" common factors.
Note that we really noticed that
Example: The rational expression:
You could multiply the numerators and denominators and end up with a quadratic over a quadratic, and then hope to simplify the result. The easiest way is to factor first:
Now rewrite so that common factors are over each other and cancel the common factors, and then simply.
The same rules apply in both cases: to multiply fractions or rational expressions the numerator of the answer is the product of the numerators and the denominator of the answer is the product of the denominators. To divide you multiply by the reciprocal.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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