SOLUTION: Find A, B, and C for the partial fraction decomposition.
{{{ ( (4x^2)-3x+7 ) / ( (x-1)((x^2) + 3) ) }}}
So far I am able to get {{{ ( A/(x-1) ) + ( (Bx + C)/(x^2+3) ) }}}
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Question 1007676: Find A, B, and C for the partial fraction decomposition.
So far I am able to get
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find A, B, and C for the partial fraction decomposition.
( (4x^2)-3x+7 ) / ( (x-1)((x^2) + 3) )
So far I am able to get::
--------
( A/(x-1) ) + ( (Bx + C)/(x^2+3) )
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= A(x^2+3) + (Bx+c)(x-1) / [(x-1)(x^2+3)]
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Equating the numerators you get::
A(x^2) + 3A + Bx^2 + cx -Bx - c = 4x^2 - 3x + 7
======
(A+B)x^2 + (c-B)x + 3A - c = 4x^2 - 3x + 7
------
Equate the corresponding coefficients to get 3 equations::
A + B = 4
C - B = -3
3A = 7
-------
A = 7/3
A+C = 1, So C = -4/3
A + B = 4, So B = 4-7/3 = 5/3
-------
Cheers,
Stan H.
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