Thực hiện phép tính (X+1)(x²-x+1); (x-3)(x²+3x+9) giúp mình với ạ
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(x – 1)(x + 1)(x + 2)
= ( x 2 + x – x – 1)(x + 2)
= ( x 2 – 1)(x + 2)
= x 2 ( x + 2) – 1.(x +2)
= x 3 + 2 x 2 – x – 2
`@` `\text {Ans}`
`\downarrow`
`x(1-x) + (x-1)^2`
`= x-x^2 + x^2 - 2x + 1`
`= (x-2x) + (-x^2 + x^2) + 1`
`= -x+1`
x ( 1 - x ) + ( x - 1 )2 = x - x2 + x2 - 2x + 1 = -x + 1 = 1 - x
\(=\left(\dfrac{1}{x\left(x+1\right)}+\dfrac{x-2}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\dfrac{x^2-2x+1}{x\left(x+1\right)}:\dfrac{x^2-2x+1}{x}\)
\(=\dfrac{1}{x+1}\)
MC: x(x + 1)
1/x - 1/(x + 1)
= (x + 1)/[x(x + 1)] - x/[x(x + 1)]
= (x + 1 - x)/[x(x + 1)]
= 1/[x(x + 1)]
a: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
\(\dfrac{3}{x-1}+\dfrac{5}{x+1}-\dfrac{x}{x^2-1}\)
\(=\dfrac{3}{x-1}+\dfrac{5}{x+1}-\dfrac{x}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{3\left(x+1\right)+5\left(x-1\right)-x}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{3x+3+5x-5-x}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{7x-2}{\left(x-1\right)\left(x+1\right)}\)
\(=\left(x^2+x-2\right)\left(x-3\right)\\ =x^3-3x^2+x^2-3x-2x+6\\ =x^3-2x^2-5x+6\)
\(\dfrac{x+1}{x^2-4}:\dfrac{x+1}{x+2}=\dfrac{x+1}{\left(x-2\right)\left(x+2\right)}:\dfrac{x+1}{x+2}=\dfrac{x+1}{\left(x-2\right)\left(x+2\right)}.\dfrac{x+2}{x+1}=x-2\)
`th1:`
`(x+1)(x^2-x+1):(x-3)(x^2+3x+9)`
`=(x^3+1^3):(x^3-3^3)`
`=(x^3+1):(x^3-27)`
`=(x^3+1)/(x^3-27)`
`=(x^3-27+28)/(x^3-27)`
`=1+28/(x^3-27)`
`**th2:`
`(x+1)(x^2-x+1)`
`=x^3+1^3=x^3+1`
`(x-3)(x^2+3x+9)`
`=x^3-3^3=x^3-27`
Minh xin loi ban nhe , ban sua lai giup minh cho x3 - 9 thanh x3 - 27