Skill: rational-expressions

Rational Expressions Practice

An endless supply of never-repeating rational-expression problems with instant feedback. Simplify, multiply, divide, and add — and always track the excluded values.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Simplify

Factor the top and bottom, cancel common factors, and state the excluded values from the original denominator.

Example: (x² − 9)/(x + 3) → x − 3, x ≠ −3

Multiply and divide

Multiply straight across (or flip-and-multiply), then simplify. Dividing also excludes the divisor’s zeros.

Example: (4/x) · (x²/8) → x/2, x ≠ 0

Add and subtract

Common denominator first — exactly like fraction arithmetic — then add the numerators and simplify.

Example: 2/x + 3/(x+1) → (5x+2)/(x(x+1)), x ≠ 0, −1

3 Watch out for these

The three mistakes students make most often on these problems.

1. Canceling terms instead of factors

Wrong: (x+5)/5 → x. Right: (x+5)/5 is already simplest — the 5s are terms, not factors. Only factors cancel.

2. Forgetting excluded values

Wrong: (x²−9)/(x+3) = x − 3, done. Right: x − 3, x ≠ −3 — the canceled factor still excludes its zero.

3. Adding without a common denominator

Wrong: 1/x + 1/y = 1/(x+y). Right: (x+y)/xy — common denominator first, always.

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