We won't need to factor anything in this example, and can simply multiply across and then simplify.
Let's look at a few examples. To begin, we'll note that the larger fraction bar is denoting division, so we will use multiplication by the reciprocal. After that, we'll factor each expression and cancel any common factors. Simplify the following expressions, and if applicable, write the restricted domain on the simplified expression. Simplify the following expression, and if applicable, write the restricted domain on the simplified expression.
Section Figure Explanation To start, we'll factor the numerator and denominator. Explanation To begin simplifying this expression, we will rewrite each polynomial in descending order. Explanation To simplify this rational function, we'll first note that both the numerator and denominator have four terms.
Explanation Note that to factor the second rational expression, we'll want to re-write the terms in descending order for both the numerator and denominator. Explanation We won't need to factor anything in this example, and can simply multiply across and then simplify. Explanation To begin, we'll note that the larger fraction bar is denoting division, so we will use multiplication by the reciprocal.
This is one of the special cases for division. Dividing Rational Expressions. Simplifying Multiplying and Dividing Adding and Subtracting. We've seen that we multiply rational expression like we multiply fractions. Multiplying and Dividing Rational Expressions. So this numerator, let's put the a plus 2's first in both the numerator and the denominator.
Step 1: Write as multiplication of the reciprocal. Step 2: Multiply the rational expressions as shown above. Note that the values that would be excluded from the domain are -6 and 0. Those are the values that makes the original denominator of the product equal to 0. Note that the values that would be excluded from the domain are 0, 2, - 4, 4, and Those are the values that make the original denominator of the quotient and the product equal to 0.
Practice Problems. At the link you will find the answer as well as any steps that went into finding that answer. Practice Problems 1a - 1b: Perform the indicated operation.
Need Extra Help on these Topics? After completing this tutorial, you should be able to: Multiply rational expressions.
In this tutorial I will be stepping you through how to multiply and divide rational expressions. In the numerator of the product we factored a GCF. In the numerator of the product we factored a GCF and a trinomial. These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems. Use the common factors to rewrite as multiplication by 1. Okay, that worked. But this time we'll simplify first, then multiply.
When using this method, it helps to look for the greatest common factor. We can factor out any common factors, but finding the greatest one will take fewer steps.
Factor the numerators and denominators. Look for the greatest common factors. Regroup the fractions to express common factors as multiplication by 1. Both methods produced the same answer. Some rational expressions contain quadratic expressions and other multi-term polynomials.
To multiply these rational expressions, factor the polynomials and then look for common factors. Just take it step by step, like in the example below.
The domain is all a -2, 0, or 2. Determine if there are any excluded values. To do this, set the denominators equal to 0 and solve for a. Regroup to express rational expressions equivalent to 1. Multiply simplified rational expressions. This expression can be left with the denominator in factored form or multiplied out. Note that in the answer above, we cannot simplify the rational expression any further. It may be tempting to express the 5s in the numerator and denominator as the fraction , but these 5s are terms that are part of a factor, not factors by themselves.
They cannot be pulled out of their expressions. Perform the indicated operation and express the answer as a simplified rational expression:. A Incorrect.
You simplify by factoring like terms in the numerator and denominator. You can only make equivalent fractions to 1 using factors, not terms.