Dividing Rational Expressions

Example 1

Find:

Solution
Step 1 Invert the second fraction and change the division symbol, ÷, to the multiplication symbol, ·.
Step 2 Factor the numerators and denominators.
Step 3 Cancel all pairs of factors common to the numerators and denominators.
Step 4 Multiply the numerators. Multiply the denominators.

Thus,

Example 2

Find:

Solution
Step 1 Invert the second fraction and change the division symbol, ÷, to the multiplication symbol, ·.
Step 2 Factor the numerators and denominators.
Step 3 Cancel all pairs of factors common to the numerators and denominators.
Step 4 Multiply the numerators. Multiply the denominators.

Thus,

Notice that is in lowest terms.