STEM PRACTICE AND EVIDENCE WORKBENCH
Find zeros of two nonconstant linear denominator factors and audit complete unique learner restriction sets.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Set each original denominator factor equal to zero. For ax+b, excluded x = -b/a; for cx+d, excluded x = -d/c. Collapse repeated values to one unique restriction within tolerance, sort the expected and learner sets, and require equal set size plus pairwise agreement. Restrictions survive algebraic cancellation because the original expression was not defined there. Supported means the learner set contains every and only the excluded real values supplied by the two factors. It does not classify the graph at those values. A repeated restriction may represent one excluded x with multiplicity, while a canceled factor can produce a hole and an uncanceled factor may produce a vertical asymptote. Inspect the original expression and later operations separately.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use before simplifying, operating on, graphing, or solving with a factored rational expression. The diagnostic makes original-domain evidence explicit and detects a missing or extra restriction. It does not factor a polynomial, parse a whole rational expression, identify complex zeros, decide whether a discontinuity is removable, draw asymptotes, or solve an equation containing the expression.
Factors x-2 and x+3 exclude 2 and negative 3, matching the entered set. Factors 2x-4 and x-2 share the same zero, so the unique set contains only 2. Fractional roots negative one half and one third are accepted within tolerance. The final factors exclude 4 and negative 5, but the learner lists only 4, so it is flagged.
Set each original denominator factor equal to zero. For ax+b, excluded x = -b/a; for cx+d, excluded x = -d/c. Collapse repeated values to one unique restriction within tolerance, sort the expected and learner sets, and require equal set size plus pairwise agreement. Restrictions survive algebraic cancellation because the original expression was not defined there.
Supported means the learner set contains every and only the excluded real values supplied by the two factors. It does not classify the graph at those values. A repeated restriction may represent one excluded x with multiplicity, while a canceled factor can produce a hole and an uncanceled factor may produce a vertical asymptote. Inspect the original expression and later operations separately.
Do not solve numerator zeros, change -b/a to b/a, list a repeated root twice as two different restrictions, lose a value after canceling, assume a canceled factor restores the original domain, omit fractional roots, or include values that merely make the numerator zero. Mark denominator zeros before simplification and carry them through every equivalent form.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
