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Simplifying Rational Expressions

In this video, we are going to simplify rational expressions.

For example:
It’s just like reducing fractions. Begin by simplifying the constants.
\frac{3}{12} would be \frac{1}{4}
Let’s now look at the exponents. The numerator is to the fourth power while the denominator is to the fifth power. As a result, there will be one x in the denominator but not in the numerator.

Now let’s look at an example where there is an operation taking place in the numerator.
Here we can separate into two separate fractions
\frac{24x^5}{6x^4} and \frac{-15x^3}{6x^4}
Then we can simplify each one and get a final answer of

When there is an operation in the denominator, we cannot simply do the same thing. Instead we must factor each term by its greatest common factor. For example:
The greatest common factor for all three terms is 3x^3. So if we take out a 3x^3 from each term, we are left with
Then, the 3x^3 in the numerator and denominator will cancel out, leaving us with a final answer of

Another type of rational expression may look like
To solve something like this, we can factor the quadratic in the numerator and denominator. In this example, we would have
From here, we could cancel out the (x-4) from the numerator and denominator, leaving us with