Rewrite Rational Expressions (Calculator)

Related Pages
Polynomial Long Division
Synthetic Division
Common Core Algebra
Common Core Mathematics

Suggested Learning Targets

• Rewrite rational expressions,
  a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) by using inspection, long division, or synthetic division and comparing coefficients.

• Use a computer algebra system for complicated examples to assist with building a broader conceptual understanding.
  

Common Core: HSA-APR.D.6

Computer Algebra System

Polynomial Division using a computer algebra system (for example Wolfram Alpha)

TI-Nspire CX CAS Polynomial Division Expand function.

Comparing Coefficients

Example:
Divide x³ + x² − 7 by x − 3 by comparing coefficients.

Rewrite the expression
x³ + x² − 7 ≡ (Ax² + Bx + C)(x − 3) + D

Expanding the right side we get,
(Ax² + Bx + C)(x − 3) + D = Ax³ + (−3A + B)x² + (−3B + C)x − 3C + D

Matching coefficients of the various powers of x on the left and right hand sides, we get
x³ + x² − 7 ≡ Ax³ + (−3A + B)x² + (−3B + C)x − 3C + D

A = 1
(−3A + B) = 1 ⇒ B = 4
(−3B + C) = 0 ⇒ C =12
− 3C + D = -7 ⇒ D = 29

The expression can then be written as
x³ + x² − 7 ≡ (x² + 4x + 12)(x − 3) + 29

Thus, (x³ + x² − 7)/(x − 3) = x² + 4x + 12 + 29/(x − 3)

Polynomial Division & Equating Coefficients

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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