Interpret terms, factors, and coefficients in polynomial and rational expressions.
Cancel common rational factors while preserving domain restrictions
Problem
Simplify \([(x~-~2)(x~+~3)]/(x~-~2)\) while preserving the original domain. State the canceled factor, exclusion, reduced formula, hole, and any remaining vertical asymptote.
Big Picture
What this problem is really about
Record the original denominator restriction before canceling a common factor. Cancellation gives a simpler formula only for allowed inputs, so the canceled zero remains missing from the graph. Evaluate the reduced formula at that excluded input to locate the hole's vertical coordinate, and inspect any denominator factors that remain to determine whether vertical asymptotes are still present.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
