decompose the following partial fraction:
(-4x^3 - 3x^2 + 12) / (x^4 + 2x^3)
the denominator should reduce to x^3 (x + 2) which gives
original fraction = A / x + B / x^2 + C / x^3 + D / (x + 2)
then: -4x^3-3x^2+12 = A(x^2)(x+2) + B (x)(x+2) + C(x+2) + D(x^3)
I can isolate and solve for C and D by plugging in x=-2 and x=0 but how can I isolate A and B??
wolfram alpha gives A as 0 and B as -3 but how can you get these numbers???
(-4x^3 - 3x^2 + 12) / (x^4 + 2x^3)
the denominator should reduce to x^3 (x + 2) which gives
original fraction = A / x + B / x^2 + C / x^3 + D / (x + 2)
then: -4x^3-3x^2+12 = A(x^2)(x+2) + B (x)(x+2) + C(x+2) + D(x^3)
I can isolate and solve for C and D by plugging in x=-2 and x=0 but how can I isolate A and B??
wolfram alpha gives A as 0 and B as -3 but how can you get these numbers???
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Consider the coefficients for x^3:
-4 = A + D
That should let you find the value of A. You can do the same with x^2 or x^1 to find the value of B.
-4 = A + D
That should let you find the value of A. You can do the same with x^2 or x^1 to find the value of B.