Rational expressions test

Factor, cancel, and never forget what x is not allowed to be.

Rational expressions test
Rational expressions test — printable test paper

The answer key prints on a separate page.

What's on this test

The three sections are one ladder. Simplifying asks for the two quadratics to be factored before anything can cancel, and the whole difficulty lives in the factoring — a student who can factor can finish. Multiplying and dividing adds the two moves that sheet does not have: cancelling across a product, and turning a division into a multiplication before anything else happens. The brackets arrive already factored there on purpose, so the new move is the only work.

How the paper is put together

The last section sets one equal to something and finds x, and it carries the half of the standard that gets dropped. Clearing a denominator can invent a solution the original equation never had, so every answer has to be checked against the values x may not take. The answer key prints those values beside each answer for that reason — a correct number under a denominator that was never allowed is not a correct answer.