Multiplying rational expressions worksheets

Multiplying two rational expressions turns them into one, and anything on top may cancel with anything underneath. These free printable worksheets practice that move, with every bracket already factored.

Multiplying rational expressions
Multiplying rational expressions worksheet — Linear brackets, roots to 9, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Canceling across is the new idea. In a single fraction, a bracket cancels with the one directly under it. Once two fractions are being multiplied they count as one, so the bracket on top of the first can cancel with the bracket under the second. A student who sees that has the main thing this page teaches.

Why this sheet works

Because the brackets are already factored, nothing here tests factoring. The answer is always one fraction, and that makes a mistake easy to spot. Dividing, which adds one step before any of this, has a sheet of its own, and the sheet that mixes the two comes after both.

How this one works

×

×
(x + 1) cancels
x ≠ −1, 5
  1. Now it is one product, so anything on top may cancel with anything underneath. (x + 1) appears in both, so it goes.
  2. What is left is .
  3. One more thing: x may not be −1 or 5. Those made a denominator zero in the original question — even the (x + 1) that canceled.