Simplify rational expressions with restrictions

What you’ll practice

This Algebra quiz focuses on simplifying rational expressions correctly and listing the restrictions (excluded values) that make denominators zero.

Each question is multiple-choice with 4 options and no timer, so you can work carefully through factoring, cancellation, and domain checks.

Common pitfalls to avoid

A frequent mistake is canceling terms that aren’t factors (you can only cancel common factors, not parts of a sum). Another is forgetting to state restrictions from the original denominator, even after simplification.

• Factor completely before canceling (GCF, trinomials, difference of squares)
• Write restrictions from the original expression, not just the simplified one
• Cancel factors only, never individual terms inside addition/subtraction
• Watch for sign errors when factoring out negatives
• Check for values that make any denominator zero after factoring

Difficulty and settings

Difficulty is balanced across easy, medium, and harder items: you’ll see straightforward cancellations alongside problems that require multi-step factoring and careful restriction tracking.

Before you start, pick your question count and choose a difficulty level (or keep Mixed) to tailor the practice to your goals—quick review, steady skill-building, or a full challenge set.