Multiplying and Dividing Rational Expressions Calculator
Divide (x+1)/(x−2) by (x−3)/(x+4) and there are three restrictions, not two. Most answers show two.
The missing one is x ≠ 3. It comes from the numerator of the fraction you divided by — because dividing by that fraction means it cannot be zero, and x = 3 would make it zero. Nothing in the question puts x − 3 under a division line, which is exactly why it gets left out. This multiplying and dividing rational expressions calculator with steps labels every restriction with where it came from, so that one cannot be missed.
What It Works Out, and Why
Multiplying rational expressions starts the same way whichever operation you picked: it factors all four parts — both tops and both bottoms — because nothing can cancel until they are products. Then, if you are dividing, it flips the second fraction and shows you the flip, since from that point it is an ordinary multiplication.
Next it lists the restrictions with their sources: first bottom, second bottom, and when you have divided, second top, marked in red. That labelling is the part no other tool does, and it is what turns a rule you half-remember into something you can see.
Then it cancels across both fractions at once. A factor on either top goes with a matching factor on either bottom, so (x²−4)/(x+3) × (x+3)/(x+2) comes down to x − 2 without any expanding. Only whole factors go — never a term from inside a bracket.
Finally it tells you how many of the restrictions cannot be read off the answer. In (x²−1)/x ÷ (x−1)/x² the answer is just x(x+1), with no denominator at all, and yet x ≠ 0 and x ≠ 1 both still hold.
The arithmetic is exact whole numbers, so no answer is ever a rounded decimal.
How to Use This Multiplying and Dividing Rational Expressions Calculator
Choose × or ÷, fill in the four boxes — top and bottom of each fraction — and press =. The line under the buttons shows how your input was read, so you can check it as you type.
The answer appears with its restrictions beneath it. One tap opens the table showing where each one came from, and under that the working step by step: factor, flip if dividing, restrictions, cancel, answer. For a single fraction on its own, the simplify rational expressions calculator does that instead.
Frequently Asked Questions
How do you multiply rational expressions?
How do you divide rational expressions?
What are the restrictions when dividing rational expressions?
Can you cancel across two different fractions?
Factor everything, flip before you divide, and write down all three sources of restrictions rather than the two you can see. That is the whole of it.