1 / 6

Partial Fraction (Decomposition)

Partial Fraction (Decomposition). Partial Fraction Decomposition of f(x)/d(x). Degree of f ≥ degree of d: Use the division algorithm to divide f by d to obtain the quotient q and remainder r and write f(x) = q(x) + r(x) d(x) d(x)

jana-valencia
Download Presentation

Partial Fraction (Decomposition)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Partial Fraction (Decomposition)

  2. Partial Fraction Decomposition of f(x)/d(x) • Degree of f ≥ degree of d: Use the division algorithm to divide f by d to obtain the quotient q and remainder r and write f(x) = q(x) + r(x) d(x) d(x) • Factor d(x) into a product of factors of the form (mx + n)u or (ax2 + bx +c)v, where ax2 + bx +c is irreducible. • For each factor (mx + n)u: The partial fraction decomposition of r(x)/d(x) must include the sum A1 + A2 + … + Au , mx + n (mx + n)2 (mx + n)u where A1, A2, …, Au are real numbers.

  3. continued • For each factor (ax2 + bx + c)v: The partial fraction decomposition of r(x)/d(x) must include the sum B1x + C1 + B2x + C2 + … + Bvx + Cv ax2 + bx + c (ax2 + bx + c)2 (ax2+bx+c)v where B1, B2,…, Bv and C1, C2,…, Cv are real numbers. The partial fraction decomposition of the original rational function is the sum of q(x) and the fraction is the sum of q(x) and the fractions in parts 3 and 4

  4. Find the partial fraction decomposition of (3x-1)/(x2-x-6)

  5. Repeated linear factors (5x2 + 20x + 6)/(x3+ 2x2 + x)

  6. Decomposing a fraction with irreducible quad. Fraction.

More Related