Passport to Advanced Math

Rational Expressions

Simplify, add, and divide rational expressions. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on rational expressions is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 For x != 0, the expression 3x^2 - 3x / 3x is equivalent to which of the following? easy 400-500 Open
2 For x != 0, the expression 5x^2 - 10x / 5x is equivalent to which of the following? easy 400-500 Open
3 For x != 0, the expression 6x^2 - 24x / 6x is equivalent to which of the following? easy 400-500 Open
4 For x != 0, the expression 2x^2 + 4x / 2x is equivalent to which of the following? easy 400-500 Open
5 For x != 0, the expression 3x^2 - 15x / 3x is equivalent to which of the following? easy 400-500 Open
6 For x != 0, the expression 6x^2 + 12x / 6x is equivalent to which of the following? easy 400-500 Open
7 For x != 0, the expression 5x^2 - 20x / 5x is equivalent to which of the following? easy 500-600 Open
8 For x != 0, the expression 2x^2 - 8x / 2x is equivalent to which of the following? easy 500-600 Open
9 For x != 0, the expression 2x^2 - 10x / 2x is equivalent to which of the following? medium 500-600 Open
10 For x != 0, the expression 3x^2 - 15x / 3x is equivalent to which of the following? medium 500-600 Open
11 For x != 0, the expression 5x^2 + 10x / 5x is equivalent to which of the following? medium 500-600 Open
12 For x != 0, the expression 2x^2 + 10x / 2x is equivalent to which of the following? medium 500-600 Open
13 For x != 0, the expression 3x^2 - 3x / 3x is equivalent to which of the following? medium 600-700 Open
14 For x != 0, the expression 6x^2 - 6x / 6x is equivalent to which of the following? medium 600-700 Open
15 For x != 0, the expression 3x^2 - 12x / 3x is equivalent to which of the following? medium 600-700 Open
16 For x != 0, the expression 6x^2 - 24x / 6x is equivalent to which of the following? medium 600-700 Open
17 For x != 0, the expression 6x^2 + 30x / 6x is equivalent to which of the following? medium 600-700 Open
18 For x != 0, the expression 5x^2 - 25x / 5x is equivalent to which of the following? medium 600-700 Open
19 For x != 0, the expression 3x^2 + 6x / 3x is equivalent to which of the following? hard 600-700 Open
20 For x != 0, the expression 5x^2 - 10x / 5x is equivalent to which of the following? hard 700-800 Open
21 For x != 0, the expression 6x^2 + 24x / 6x is equivalent to which of the following? hard 700-800 Open
22 For x != 0, the expression 3x^2 + 6x / 3x is equivalent to which of the following? hard 700-800 Open
23 For x != 0, the expression 6x^2 - 12x / 6x is equivalent to which of the following? hard 700-800 Open
24 For x != 0, the expression 4x^2 + 12x / 4x is equivalent to which of the following? hard 700-800 Open
25 For x != 0, the expression 4x^2 + 12x / 4x is equivalent to which of the following? hard 700-800 Open