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Course: Algebra (all content) > Unit 13
Lesson 2: Simplifying rational expressions- Reducing rational expressions to lowest terms
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Simplifying rational expressions (advanced)
Have you learned the basics of rational expression simplification? Great! Now gain more experience with some trickier examples.
What you should be familiar with before taking this lesson
A rational expression is a ratio of two polynomials. A rational expression is considered simplified if the numerator and denominator have no factors in common.
If this is new to you, we recommend that you check out our intro to simplifying rational expressions.
What you will learn in this lesson
In this lesson, you will practice simplifying more complicated rational expressions. Let's look at two examples, and then you can try some problems!
Example 1: Simplifying
Step 1: Factor the numerator and denominator
Here it is important to notice that while the numerator is a monomial, we can factor this as well.
Step 2: List restricted values
From the factored form, we see thatand .
Step 3: Cancel common factors
Step 4: Final answer
We write the simplified form as follows:
for
Main takeaway
In this example, we see that sometimes we will have to factor monomials in order to simplify a rational expression.
Check your understanding
Example 2: Simplifying
Step 1: Factor the numerator and denominator
While it does not appear that there are any common factors, and are related. In fact, we can factor out of the numerator to reveal a common factor of .
Step 2: List restricted values
From the factored form, we see that and .
Step 3: Cancel common factors
The last step of multiplying the into the numerator wasn't necessary, but it is common to do so.
Step 4: Final answer
We write the simplified form as follows:
Main takeaway
The factors and are opposites since .
In this example, we saw that these factors canceled, but that a factor of was added. In other words, the factors and canceled to .
In general opposite factors and will cancel to provided that .
Check your understanding
Let's try some more problems
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