You may cancel a factor and you may not cancel a term, and (x² − 81) ÷ (x − 9) is where the difference bites. These free printable worksheets show the illegal cancellation written out and ask which answer is correct.
If they get stuck
The answer key prints on a separate page.
Factorizing first is what makes canceling legal, and the answer key shows that step rather than asserting the rule. Once the top is written as two brackets, the one that matches the bottom leaves and the other one is the answer — and which one leaves depends on the sign underneath, so the answer is not always the same shape.
Adding two algebraic fractions is the same discipline from the other end. The denominators have to be made common rather than added, and the four wrong answers are the four shortcuts: bottoms added, tops and bottoms both added, tops multiplied, and the sum used as the common denominator.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Algebraic fractions, step by step