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If five is subtracted from three times a certain number, the result is 10. What is the number

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

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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fracciones parciales 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)

Crear un modelo para la fracción parcial usando el denominador (x+1)(x−4)

x(x+1)(x−4) =a₀x+1 +a₁x−4

Multiplicar la ecuación por el denominador

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

Simplificar

x=a₀(x−4)+a₁(x+1)

Resolver las parámetros desconocidos sustituyendo las raíces reales del denominador: −1, 4

Para la raíz del denominador −1: a₀=15

Para la raíz del denominador 4: a₁=45

a₀=15 , a₁=45

Sustituir las soluciones a los parámetros de la fracción parcial para obtener el resultado final

15 x+1 +45 x−4

Simplificar

15(x+1) +45(x−4)

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

If five is subtracted from three times a certain number, the result is 10. What is the number

Solution

Solution steps

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