If frac{5x^2+2}{x^3+x}=frac{A_1}{x}+frac{A_2x | vedclass

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(C) Given that,$\frac{5x^2+2}{x(x^2+1)} = \frac{A_1}{x} + \frac{A_2x+A_3}{x^2+1}$ Multiplying both sides by $x(x^2+1)$,we get: $5x^2+2 = A_1(x^2+1) +

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$(2, 3, 0)$

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(C) Given that,$\frac{5x^2+2}{x(x^2+1)} = \frac{A_1}{x} + \frac{A_2x+A_3}{x^2+1}$ Multiplying both sides by $x(x^2+1)$,we get: $5x^2+2 = A_1(x^2+1) + (A_2x+A_3)x$ $5x^2+2 = A_1x^2 + A_1 + A_2x^2 + A_3x$ $5x^2+2 = (A_1+A_2)x^2 + A_3x + A_1$ Comparing the coefficients of $x^2$,$x$,and the constant term on both sides: Constant term: $A_1 = 2$ Coefficient of $x$: $A_3 = 0$ Coefficient of $x^2$: $A_1 + A_2 = 5$ $\Rightarrow 2 + A_2 = 5$ $\Rightarrow A_2 = 3$ Thus,$(A_1, A_2, A_3) = (2, 3, 0)$.

If $\frac{5x^2+2}{x^3+x}=\frac{A_1}{x}+\frac{A_2x+A_3}{x^2+1}$,then $(A_1, A_2, A_3) = $

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