Question

Tìm giá trị của x, biết: \(\frac{1}{x\left(x+1\right)}=\frac{1}{x}+\frac{1}{2011}.\)

x = ....

Answer 1

(x khác 0,-1)

\(\Leftrightarrow\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x}+\frac{1}{2011}\Leftrightarrow-\frac{1}{x+1}=\frac{1}{2011}\Leftrightarrow x+1=-2011\Leftrightarrow x=-2012.\)

Answer 2

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

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

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

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

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

\(\Rightarrow2011.\left(-1\right)=\left(x+1\right).1\)

\(\Rightarrow-2011=x+1\)

\(\Rightarrow x=-2011-1\)

\(\Rightarrow x=-2012\)

Answer 3

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

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

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

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

\(\Rightarrow x+1=-2011\)

\(\Rightarrow x=-2011-1=-2012\)