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Math

Attribution

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License.

Dividing Rational Expressions: 

In order to divide rational expressions, perform the following steps:
Step 1) Factor the numerators and the denominators of all the fractions in the expression.
Step 2) Convert the division to multiplication by multiplying the first fraction by the reciprocal of the second fraction.
Step 3) Multiply the numerators with each other and multiply the denominators with each other.
Step 4) Simplify the results.

 

Example: Divide.
Step 1) We can not factor the numerators or the denominators of the two fractions any further. So, we leave the fractions as they are.
Step 2) Multiply the first fraction by the reciprocal of the second fraction.

Step 3) Multiply the numerators with each other and the denominators with each other

Step 4) Simplify the result.

.

 

Example: Divide  State the non-permissible values.
Step 1) We factor the numerator and the denominator in the first fraction.

therefore, we have

The original division becomes:

Step 2) Now, we convert division to a multiplication:

Step 3) We multiply the numerators together and the denominators together:

Step 4) We simplify the result.

.

To find the non-permissible values, one has to set the denominator of the first fraction and second fraction as well as the numerator of the second fraction equal to zero and solve for the variable:

Now, we set the denominator of the second fraction equal to zero and solve for x:

So, the non-permissible values are

 

ATTENTION!! In order to find the non-permissible values of a division, one has to set the denominator of the first fraction and second fraction as well as the numerator of the second fraction equal to zero and solve for the variable.
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