Multiplying and dividing rational expressions
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Multiplying and Dividing Rational Expressions. Multiplying and Dividing Fractions. Multiply Numerators. Multiply:. Multiply Denominators. Divide:. Multiply by the reciprocal (flip). Remember to Simplify!. Example 1. Simplify the following expressions:.

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Multiplying and dividing fractions
Multiplying and Dividing Fractions

Multiply Numerators

Multiply:

Multiply Denominators

Divide:

Multiply by the reciprocal (flip)

Remember to Simplify!


Example 1
Example 1

  • Simplify the following expressions:

The techniques we use to simplify a fraction without variables (Finding the greatest common FACTOR) is the same we will use to simplify fractions with variables.


Example 2
Example 2

These are just the values of x that make the expression undefined.

Simplify:

Half the work is done. It is already factored.

Combine the fractions by multiplying

Rewrite any factors if they are raised to a power

Cancel common factors


Example 3
Example 3

These are just the values of x that make the expression undefined.

Simplify:

Multiply by the reciprocal (Flip the fraction)

Can NOT cancel since its not in factored form.

Factor

Make sure to Factor Completely

Cancel common factors



Example 31
Example 3

These are just the values of x that make the expression undefined.

Simplify:

Can NOT cancel since its not in factored form.

Multiply by the reciprocal (Flip the fraction)

Almost the same as x – 5

Factor

Make sure to Factor Completely

TRICK: Factor out -1 to make it the same.

Cancel common factors


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