Dividing rational expressions worksheets

Dividing rational expressions is multiplying with one step first: turn the second fraction over. These free printable worksheets practice doing that in the right order, with every bracket already factored.

Dividing rational expressions
Dividing 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

The flip has to come first, and the reason is that canceling across a division sign is not a valid move. A student who skips the flip will sometimes still land on the right answer, and that is what makes the habit hard to catch by marking alone. Asking for the flipped line to be written out each time makes it visible.

Why this sheet works

After the flip the question is a multiplication, and it cancels the same way. Every answer is one fraction. If the flip is the new part, it helps to have the multiplying sheet done first, so that this page has only one new thing on it.

How this one works

÷

÷
×
×
(x + 1) cancels
x ≠ −1, 5
  1. Dividing by a fraction is multiplying by it upside down, so do that first. Turn over and change the ÷ to a ×.
  2. Now it is one product, so anything on top may cancel with anything underneath. (x + 1) appears in both, so it goes.
  3. What is left is .
  4. 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.