Rational ExpressionsFractions with algebra in them — and the values that are forbidden.10th GradeA rational expression is a fraction of polynomials.Factor first, cancel common factors, and excludeanything that makes the original denominator zero.(x² − 9)/(x + 3) = x − 3, x ≠ −3(x² − 9)/(x + 3)x − 3, x ≠ −3Factor the top as (x+3)(x−3).Multiplyfactor, cancel, multiplyCancel across before multiplying.Divideflip the second, then multiplySame rule as numeric fractions.Add or subtractcommon denominator firstExactly like numeric fractions.THE COMMON MISTAKE✗ cancelling (x + 3)/(x + 5) to 3/5✓ you cannot cancel terms, only factorsCancelling works across multiplication, never across addition.The restriction comes from the ORIGINAL denominator, before anycancelling.Rational Expressionslearnposters.com
Rational Expressions — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Rational Expressions poster

The rule, 4 worked examples, and the mistake everyone makes.

The restriction comes from the ORIGINAL denominator, before any cancelling.

Questions about the Rational Expressions poster

What’s on the Rational Expressions poster?
The rule, 4 worked examples, and the mistake everyone makes. A rational expression is a fraction of polynomials. Factor first, cancel common facto…; (x² − 9)/(x + 3) = x − 3, x ≠ −3; Multiply = factor, cancel, multiply; Divide = flip the second, then multiply; Add or subtract = common denominator first; Common mistake: cancelling (x + 3)/(x + 5) to 3/5 → you cannot cancel terms, only fac…. The restriction comes from the ORIGINAL denominator, before any cancelling.
Who is the Rational Expressions poster for?
Rational Expressions is filed under 10th Grade (ages 15–16), so it matches what that year asks a child to remember. It is equally useful to an older student revisiting math, and to the parent or teacher answering the question at the kitchen table.
When should you use the Rational Expressions poster?
State the restrictions before simplifying. After simplifying, they are invisible. A wall chart earns its place by being glanceable from where the work is happening, so Rational Expressions belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Rational Expressions?
Sequences and Series, Completing the Square and Complex Numbers sit alongside Rational Expressions in the 10th Grade set. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Sequences and SeriesCompleting the SquareComplex Numbers
Is the Rational Expressions poster free to download and print?
Yes. Rational Expressions downloads as a free PDF with no account, no email and no watermark, like everything else in the 10th Grade set. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Rational Expressions poster print at?
Rational Expressions is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Rational Expressions loses nothing.Printing guide

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