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# Partial Fractions

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Enter (A,B,C) in order below if A, B, and C are the coefficients of the partial fractions expansion of (2x^2 + 3x - 5)/(x(x^2 - 1)) = A/x + B/(x - 1) + C/(x + 1).

Feb 5, 2022

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$$\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A}{x} + \frac{B}{(x - 1)} + \frac{C}{(x + 1)}\\ \frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)}{x(x - 1)(x + 1)} + \frac{Bx(x + 1)}{(x - 1)(x + 1)x} + \frac{C(x - 1)x}{(x + 1)(x - 1)x}\\ \frac{2x^2 + 3x - 5}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)+Bx(x + 1)+C(x - 1)x}{x(x - 1)(x + 1)} \\$$

Now expand and equate coefficients

LaTex:

\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A}{x} + \frac{B}{(x - 1)} + \frac{C}{(x + 1)}\\
\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)}{x(x - 1)(x + 1)} + \frac{Bx(x + 1)}{(x - 1)(x + 1)x} + \frac{C(x - 1)x}{(x + 1)(x - 1)x}\\
\frac{2x^2 + 3x - 5}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)+Bx(x + 1)+C(x - 1)x}{x(x - 1)(x + 1)} \\

Feb 5, 2022