다명의 (2x+3)^3-4x^3

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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partial fractions x(x+1)(x−4)

Solution

15(x+1) +45(x−4)

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Solution steps

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x(x+1)(x−4)

Create the partial fraction template using the denominator (x+1)(x−4)

x(x+1)(x−4) =a₀x+1 +a₁x−4

Multiply equation by the denominator

x(x+1)(x−4)(x+1)(x−4) =a₀(x+1)(x−4)x+1 +a₁(x+1)(x−4)x−4

Simplify

x=a₀(x−4)+a₁(x+1)

Solve the unknown parameters by plugging the real roots of the denominator: −1, 4

For the denominator root −1: a₀=15

For the denominator root 4: a₁=45

a₀=15 , a₁=45

Plug the solutions to the partial fraction parameters to obtain the final result

15 x+1 +45 x−4

Simplify

15(x+1) +45(x−4)

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

다명의 (2x+3)^3-4x^3

Solution

Solution steps

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