Rational expressions and original restrictions

Rational expressions and original restrictions

Strengthen the algebra habits needed for rational functions by simplifying, multiplying and dividing rational expressions while preserving every original restriction. This set treats domain information as part of an answer, not as an optional note after cancellation.

Questions begin with denominator zeros and common factors, then progress to reversed subtraction, quadratic factoring, products and division by another expression. You will distinguish a zero dividend from a zero divisor and compare a simplified formula with the natural domain of its original form. A geometric context adds physical restrictions beyond those required by algebra alone.

Prerequisites

Review polynomial factoring, including differences of squares and quadratic trinomials. Record exclusions before cancelling, and remember that terms in a sum are not common factors.

How to study

Solve on paper, evaluate every select-all statement, and use the explanations to check both the calculation and its conditions. This practice supports later work with rational functions and equations without requiring graph analysis or equation-solving methods here.