Adding and subtracting rational expressions

Adding and subtracting rational expressions

Practise combining algebraic fractions accurately, from shared denominators to factored and repeated denominators. This precalculus foundation set emphasises the structure of a least common denominator and the need to scale numerators and denominators together.

Questions develop subtraction with parentheses, opposite linear factors, repeated powers and cancellation after combining fractions. You will distinguish a least common denominator from another valid common denominator, check whether a transformation introduces a new restriction, and use coefficient comparison to decide whether a proposed identity can hold.

Preparation

Review factoring, multiplication of rational expressions and original-domain restrictions. Write the exclusions first and distribute every minus sign across the entire numerator. A shared-fee context connects the symbolic rules to the meaning of a fraction.

Worked review

Single-select and select-all questions include stepwise explanations and checks. Use the feedback to separate errors in choosing a denominator, distributing signs and cancelling factors. The set stays within expression algebra and prepares you for complex fractions without assuming rational-equation techniques.