Cancelling Factors: Why the Missing Input Stays Missing
Learn why cancelling a factor preserves an excluded input and distinguish a function value from a limit, with a worked example and three self-checks for Concordia MATH 203 and McGill MATH 140.
Subject area
Algebra & Precalculus Tutoring
Build the algebra, function, and trigonometry skills needed for calculus, physics, and other quantitative courses.
Topics covered
Basic and college algebraEquations and inequalitiesPolynomial and rational functionsFunctions, graphs, and transformationsExponents and logarithmsTrigonometryAnalytic geometryVectorsPrecalculusMathematics preparation for physics
Common difficulties
- Manipulating expressions while respecting restrictions
- Understanding domains, inverses, and graph transformations
- Using trigonometric identities confidently
How tutoring can help
We locate gaps in prerequisite skills and rebuild them through clear examples. Practice connects symbolic work to graphs and applications so each technique has context.
Simplification does not erase a restriction
Simplify (x² − 9)/(x − 3) and decide whether the original expression is defined at x = 3.
Work through the reasoning
Factoring the numerator gives (x − 3)(x + 3). Cancelling the common factor produces x + 3 only for x ≠ 3. The original graph has a hole at (3, 6), not a value there. Keeping track of the domain is essential before studying limits.
Prepare for your lesson
Try a rational expression, a logarithmic equation and a unit-circle question without notes. Mark where you need a rule or a sign check. This small diagnostic helps separate missing prerequisites from a problem with function notation.
An original Nablio example, not a university exam question. Your current course outline determines the material to focus on.
Independent practice
Free resources to work through
Before Calculus: 10 Algebra Skills You Should Know
Ten essential algebra skills with worked examples, common mistakes and self-checks: a practical starting point before university or CEGEP calculus.
Concordia MATH 203 Readiness Checklist
Check your algebra, functions and trigonometry before MATH 203 with original questions, explained answers and a focused review plan.
Exam preparation
Book a LessonReview with a clear plan.
Exam preparation can target recurring algebra errors, function analysis, and the main precalculus question types.
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