x³ - x² - x = 1/3 
<=> x³ = x² + x + 1/3 
<=> 3x³ = 3(x² + x + 1/3) 
<=> 3x³ = 3x² + 3x + 1 
<=> 3x³ + x³ = x³ + 3x² + 3x + 1 
<=> 4x³ = (x + 1)³ 
<=> ³√(4x³) = ³√(x + 1)³ 
<=> ³√4.x = x + 1 
<=> ³√4.x - x = 1 
<=> x(³√4 - 1) = 1 
<=> x = 1/(³√4 - 1) 

Ta có \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

\(\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)

\(\Rightarrow x^2+2x-3=x^2-4\)

\(\Rightarrow x^2-x^2+2x=-4+3\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=-\frac{1}{2}\)

Vậy \(x=-\frac{1}{2}\)

\(x^2\left(x+1\right)+\left(x+1\right)=y^3\)

\(\left(x+1\right)\left(x^2+1\right)=y^3\)

\(\left(x+1\right)\left(x^2+1\right)-y^3=0\)

\(\orbr{\begin{cases}x+1=0\\x^2+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x^2=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\kothoaman\end{cases}}}\)

\(\Rightarrow\hept{\begin{cases}x=-1\\y^3=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-1\\y=0\end{cases}}\)

Vậy x = -1, y =0

\(\Rightarrow x+\frac{1}{2}+x+\frac{1}{3}+x+\frac{1}{4}+x+\frac{1}{5}-x+\frac{1}{6}=0\)  

\(\Rightarrow3x+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\)

k cho minh

\(x+\frac{1}{2}+x+\frac{1}{3}+x+\frac{1}{4}+x+\frac{1}{5}=x+\frac{1}{6}\)

\(\Leftrightarrow x+\frac{1}{2}+x+\frac{1}{3}+x+\frac{1}{4}+x+\frac{1}{5}-x-\frac{1}{6}=0\)

\(\Leftrightarrow3x+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}-\frac{1}{6}=0\)

Tính ra nhé !

\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}-\dfrac{x-3}{2009}=\dfrac{x-4}{2008}\)

<=> \(\left(\dfrac{x-1}{2011}-1\right)+\left(\dfrac{x-2}{2010}-1\right)-\left(\dfrac{x-3}{2009}-1\right)=\left(\dfrac{x-4}{2008}-1\right)\)

<=> \(\dfrac{x-2012}{2011}+\dfrac{x-2012}{2010}-\dfrac{x-2012}{2009}-\dfrac{x-2012}{2008}=0\)

<=> \(\left(x-2012\right)\left(\dfrac{1}{2011}+\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\right)=0\)

<=> x - 2012 = 0

<=> x = 2012

Hay lắm em

Trả lời đúng , mình sẽ cho 5 vote

lmj có sao mà vote :v

x(x+1)-(x-1)(x+2)=8

\(\Leftrightarrow\)\(x^2+x-x^2-2x+x+2=8\)

\(\Leftrightarrow0x=6\left(ptvn\right)\)

\(\Rightarrow S=\varnothing\)

x(x-3)-x(x+1)=12

<=>x²-3x-x²-x=12

<=>-4x=12

<=>x=-3

`x-(5/6 -x) =x-2/3`

`x-5/6 +x -x+2/3 =0`

`x = 5/6-2/3 = 5/6 -4/6 = 1/6`

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