Question

\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}+\frac{1}{2011}\)

Tìm x

Answer 1

có 1/x(x+1)= 1/x + 1/2011

 => 1/x - 1/x+1=1/x+ 1/2011

=> -1/x+1=1/x-1/x+1/2011

=>-1/x+1=1/2011

=> -(x+1)=2011

=> x+1 = -2011

=>x=-2011-1=-2012

vậy x= -2012

Answer 2

2010

Answer 3

\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}+\frac{1}{2011}\)

\(\frac{1}{x\left(x+1\right)}-\frac{1}{x}=2011\)

\(\frac{1-x+1}{x\left(x+1\right)}=\frac{1}{2011}\)

\(\frac{x}{x\left(x+1\right)}=\frac{1}{2011}\)

x(x+1)=2011x

=>x+1=2011

=>x=2010