Partial Fraction Decomposition

1. Partial Fraction Decomposition Roseleen Syron, Alexa Sikoryak, Habin Choi, Jennie Park

2. Partial Fraction Decomposition used with rational functions<rational function>-r(X)=p(X)/q(X) -degree of p(X) < degree of q(X) A linear gets A during distribution A non linear gets Ax+B during distribution

3. Linear Problems Linear, non repeating_____________ = A + B + C (x-a)(x-b)(x-c) (x-a) (x-b) (x-c) Linear, repeating__________ = A + B + C (x-a)2(x-b) (x-a) (x-a)2 (x-b)

4. Non Linear Problems Non linear, non repeating_______________ = A + Bx+C (x-a)(bx2+cx+d) (x-a) (bx2+cx+d) Non linear, repeating________________ =(x-a)(bx2+cx+d)2 A + Bx+C + Dx+E(x-a) (bx2+cx+d) (bx2+cx+d)2

5. Steps • Factor denominator completely • Separate each factor as its own denominator • Determine whether each is linear or nonlinear • The ones that are liner (non-repeating) get a single letter in the numerator. • The ones that are non linear get two letters, one having a variable attached • Solve for the numerator

6. Demonstration https://www.youtube.com/watch?v=pZ9FfGy3Cfw

7. Examples : Linear, repeat 3x2-2x+8x3-x2+2x-2

8. Examples : X Linear, X repeat 3xx3+33

9. Answers 3 + -2 x-1 x2 + 2 -1 + x+3 x+3 x2 + 3x+9

10. Thank You