1. Home
  2. >Math 30-2 (Alberta)
  3. >Rational Expressions
Help

Partial fraction decomposition

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/1
?
Intros
Lessons
  1. Introduction to Partial Fraction Decomposition
    What is partial fraction decomposition?
0/8
?
Examples
Lessons
  1. Case 1: Denominator is a product of linear factors with no repeats

    Find the partial fractions of:

    1. x+7(x+3)(x−1)\frac{x + 7}{(x + 3)(x - 1)}
    2. 4x+3x2+x\frac{4x + 3}{x^{2} + x}
  2. Case 2: Denominator is a product of linear factors with repeats

    Find the partial fractions of :

    1. 3x2−5(x−2)3\frac{3x^{2} - 5}{(x - 2)^{3}}
    2. 2x−1x2+10x+25\frac{2x - 1}{x^{2} + 10x + 25}
  3. Case 3: Denominator contains irreducible quadratic factors with no repeats

    Find the partial fractions of :

    2x2+5x+8x3−8x\frac{2x^{2} + 5x + 8}{x^{3} - 8x}

    1. Case 4: Denominator contains irreducible quadratic factors with repeats

      Find the partial fractions of:

      3x4+x3+1x(x2+1)2\frac{3x^{4} + x^{3} + 1}{x(x^{2} + 1)^{2}}

      1. First perform long division, then partial fraction decomposition

        Find the partial fractions of:

        1. x3−3x2+4xx2−3x2\frac{x^{3} - 3x^{2} + 4x}{x^{2} - 3x 2}
        2. 2x2+14x+24x2+6x−16\frac{2x^{2} + 14x + 24}{x^{2} + 6x - 16}
      Topic Notes
      ?

      ∙\bullet Partial fraction decomposition expresses a rational function f(x)g(x)\frac{f(x)}{g(x)}, where f(x)f(x) and g(x)g(x) are polynomials in xx, as a sum of simpler fractions.

      ∙\bullet Partial fraction decomposition only applies to proper fractions in which the degree of the numerator is less than that of the denominator.

      Basic Concepts
      ?
      Related Concepts
      ?