houyuyao125
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Plz help!
Review the work showing the first few steps in writing a
partial fraction decomposition
What are the values of A, B, C, and D?
x+8x- 3/(x^2+5)^2=Ax+B/x^2+5+Cx+D(x^2+5)^2
O A = 0; B = 1; C = -3; D = 3
O A = 0; B = 1; C = 3, D = -3
O A= 1; B = 0; C = -3; D = 3
O A = 1; B = 0; C = 3, D = -3
x3 + 8x – 3 = (AX + B)(x2 + 5) + Cx+D
x3 + 8x – 3 = AX2 + 5AX + Bx2 + 5B + CX + D

Plz help Review the work showing the first few steps in writing a partial fraction decomposition What are the values of A B C and D x8x 3x252AxBx25CxDx252 O A 0 class=

Respuesta :

reinhard10158

Step-by-step explanation:

let's look at the last line :

x³ + 8x - 3 = Ax³ +5Ax + Bx² + 5B + Cx + D

since we find A, B, C, and D by simply comparing the factors of the various terms in x (or constants) in both sides of the equation, we need to combine a few terms on the right hand side (so that we have one term per x exponent grade).

x³ + 8x - 3 = Ax³ + (5A + C)x + Bx² + (5B + D)

by comparing now both sides, to make both sides truly equal, the factors have to be equal.

A = 1 (the same as for x³ on the left hand side).

B = 0 (a we have no x² on the left side).

5A + C = 8 (a 8 is the factor of x in the left side).

5×1 + C = 8

5 + C = 8

C = 3

5B + D = -3 (as the constant term is -3 on the left side).

5×0 + D = -3

D = -3

so, the 4th answer option is correct.

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