Casio fx-3650P and fx-CG50: Partial Fraction Decomposition
Casio fx-3650P (II) Program: Partial Fraction Decomposition
The following program calculates the coefficients decomposition, X and Y, as follows:
(A ∙ t + B) ÷ ((t + C) ∙ (t + D)) = X ÷ (t + C) + Y ÷ (t + D)
Note: C ≠ D
where:
X = (B - A ∙ C) ÷ (D - C)
Y = A - X
Program: (35 Steps)
? → A : ? → B : ? → C : ? → D :
( B - A C ) ÷ ( D - C → X ◢ A - X → Y
Example:
(2t - 3) ÷ ((t - 1)(t + 4)) = -0.2÷(t-1) + 2.2÷(t + 4)
A = 2, B = -3, C = -1, D = 4
Result: -0.2, 2.2
The above algorithm should be good for the fx-7000G, fx-50FII, fx-4000P, fx-5800P, and other programming and graphing calculators (modifications may be necessary).
Casio fx-CG50 Program: PARTFRAC
The code listed will also be good for the fx-9750G/fx-9860G series.
The program PARTFRAC, 720 bytes, will execute partial fraction decomposition of any of the three types:
(1) (A ∙ x + B)÷((x + C) ∙ (x + D)) = R÷(x + C) + S÷(x + D)
Inputs: A, B, C, D
Outputs: R, S
[[ R ] [ S ]] = [ [ D, C ] [ 1, 1 ] ]^(-1) ∙ [ [ B ] [ A ] ]
(2) (A ∙ x^2 + B ∙ x + C)÷((x + D)^2 ∙ (x + E)) = R÷(x + D)^2 + S÷(X + D) + T÷(x + E)
Inputs: A, B, C, D, E
Outputs: R, S, T
[[ R ][ S ][ T ]] = [[ E, D ∙ E, D^2 ][ 1, D + E, 2 ∙ D ][ 0, 1, 1 ]]^-1) ∙ [[ C ][ B ][ A ]]
(3) (A ∙ x^2 + B ∙ x + C)÷((x+D)∙(x+E)∙(x+F)) = R÷(x+D) + S÷(x+E) + T÷(x+F)
Inputs: A, B, C, D, E, F
Outputs: R, S, T
[[ R ][ S ][ T ]] =
[[ E ∙F, D ∙ F, D ∙ E ][ E+F, D+F, D+E ][ 1, 1, 1 ]]^-1) ∙ [[ C ][ B ][ A ]]
Program Listing:
'ProgramMode:RUN
"2021-11-05 EWS"
"PARTIAL FRACTION"
"N(X)/D(X)"◢
Lbl 0
Menu "DENOMINATOR?","(X+C)(X+D)",1,"(X+D)_^<2>_(X+E)",2,"(X+D)(X+E)(X+F)",3,"EXIT",E
Lbl 1
"(AX+B)/((X+C)(X+D))"◢
"A"?->A
"B"?->B
"C"?->C
"D"?->D
[[D,C][1,1]]^<-1>*[[B][A]]->Mat A
Mat A[1,1]->R
Mat A[2,1]->S
"=R/(X+C)+S/(X+D)"◢
"R="
R◢
"S="
S◢
Goto 0
Lbl 2
"(AX_^<2>_+BX+C)/((X+D)_^<2>_(X+E))"◢
"A"?->A
"B"?->B
"C"?->C
"D"?->D
"E"?->E
[[E,D*E,D^<2>][1,D+E,2*D][0,1,1]]^<-1>*[[C][B][A]]->Mat A
Mat A[1,1]->R
Mat A[2,1]->S
Mat A[3,1]->T
"=R/(X+D)_^<2>_+S/(X+D)+T/(X+E)"◢
"R="
R◢
"S="
S◢
"T="
T◢
Goto 0
Lbl 3
"(AX_^<2>_+BX+C)/((X+D)(X+E)(X+F))"◢
"A"?->A
"B"?->B
"C"?->C
"D"?->D
"E"?->E
"F"?->F
[[E*F,D*F,D*E][E+F,D+F,D+E][1,1,1]]^<-1>*[[C][B][A]]->Mat A
Mat A[1,1]->R
Mat A[2,1]->S
Mat A[3,1]->T
"=R/(X+D)+S/(X+E)+T/(X+F)"◢
"R="
R◢
"S="
S◢
"T="
T◢
Goto 0
Lbl E
"DONE."
Download (fx-CG 50):
https://drive.google.com/file/d/1hAIFrlX6xLMYPRiLz_dt7hpiP64CxmKC/view?usp=sharing
Examples To Try:
Type 1:
(8 ∙ x + 3) ÷((x + 4) ∙ (x - 6)) = (29/10) ÷ (x + 4) + (51/10) ÷ (x - 6)
Type 2:
(x^2 + 4 ∙x + 5) ÷ ((x - 3)^2 ∙ (x + 1)) =
(13/2) ÷ (x - 3)^2 + (7/8) ÷ (x - 3) + (1/8) ÷ (x + 1)
Type 3:
(2 ∙ x^2 + 3 ∙ x - 1) ÷ ((x - 1) ∙ (x + 2) ∙ (x + 4)) =
(4/15) ÷ (x - 1) + (-1/6) ÷ (x + 2) + (19/10) ÷ (x + 4)
Eddie
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