OML Search

Rewrite Rational Expressions (Calculator)


Videos and lessons to help High School students learn how to rewrite simple rational expressions in different forms;
write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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

Related Topics:
Polynomial Long Division

Synthetic Division

Common Core (Algebra)

Common Core for Mathematics

Computer Algebra System

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

Ti-Nspire CX CAS Polynomial Division Expand function.

Comparing Coefficients

Divide  x3+x27 by  x3 by comparing coefficients.

Rewrite the expression
x3+x27(Ax2+Bx+C )(x3)+D

Expanding the right side we get,
(Ax2+Bx+C )(x3)+D = Ax3 + (3A+B)x2+(3B+C )x3C + D

Matching coefficients of the various powers of x on the left and right hand sides, we get
+x27 ≡ Ax3 + (3A+B)x2+(3B+C )x3C + 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

Thus, (x3+x27)/( x3) = (x2+4x+12) + 29/( x3)

Polynomial Division & Equating Coefficients


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

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

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines