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) ) }}}

Algebra ->  Matrices-and-determiminant -> 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) ) }}}      Log On


   

Question 1007676: Find A, B, and C for the partial fraction decomposition.
+%28+%284x%5E2%29-3x%2B7+%29+%2F+%28+%28x-1%29%28%28x%5E2%29+%2B+3%29+%29+
So far I am able to get +%28+A%2F%28x-1%29+%29+%2B+%28+%28Bx+%2B+C%29%2F%28x%5E2%2B3%29+%29+
Answer by stanbon(75887) About Me  (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::
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( 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
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(A+B)x^2 + (c-B)x + 3A - c = 4x^2 - 3x + 7
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Equate the corresponding coefficients to get 3 equations::
A + B = 4
C - B = -3
3A = 7
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A = 7/3
A+C = 1, So C = -4/3
A + B = 4, So B = 4-7/3 = 5/3
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Cheers,
Stan H.