Rewriting Rational Expressions
Aligned to A-APR.D.6 — Common Core State Standards for Mathematics.
What this lesson teaches
A rational expression can be rewritten as a quotient plus a remainder over the divisor, in the form q(x) + r(x)/b(x). Use polynomial long division, or factor and cancel when the numerator factors evenly.
Worked example
Rewrite (x^2 + 3x + 5)/(x + 1). Divide: x^2 + 3x + 5 by (x + 1). x times (x + 1) is x^2 + x, leaving 2x + 5; 2 times (x + 1) is 2x + 2, leaving remainder 3. So the result is x + 2 + 3/(x + 1).
Practice questions
- Simplify (x^2 − 4)/(x − 2) by factoring.
- Divide (x^2 + 5x + 6)/(x + 2).
- Rewrite (2x^2 + x − 1)/(x + 1) as quotient plus remainder.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Reescribir Expresiones Racionales
Una expresión racional se puede reescribir como un cociente más un residuo sobre el divisor, en la forma q(x) + r(x)/b(x). Usa la división larga de polinomios, o factoriza y cancela cuando el numerador se factoriza de forma exacta.
Ejemplo: Reescribe (x^2 + 3x + 5)/(x + 1). Divide x^2 + 3x + 5 entre (x + 1). x por (x + 1) es x^2 + x, deja 2x + 5; 2 por (x + 1) es 2x + 2, deja residuo 3. Así que el resultado es x + 2 + 3/(x + 1).
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