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laplace ngược (x^2-6x+8)/(x-4)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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inverse laplace x²−6x+8x−4

Solution

δ′(t)−2δ(t)

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Solution steps

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L⁻¹{x²−6x+8x−4 }

Take the partial fraction of x²−6x+8x−4 : x−2

=L⁻¹{x−2}

Use the linearity property of Inverse Laplace Transform:
For functions f(s), g(s) and constants a, b: L⁻¹{a·f(s)+b·g(s)}=a·L⁻¹{f(s)}+b·L⁻¹{g(s)}

=L⁻¹{x}−L⁻¹{2}

L⁻¹{x}: δ′ (t)

L⁻¹{2}: 2δ(t)

=δ′ (t)−2δ(t)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

laplace ngược (x^2-6x+8)/(x-4)

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