Hình như để như này :
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)
\(\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=0\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\right)=0\)
Do \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}>0\Rightarrow x+2015=0\)
\(\Leftrightarrow x=-2015\)
Vậy \(x=-2015\)
Tìm x, biết: \(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)
Đề như trên có đúng không bạn? ._.
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)
\(\frac{x+1}{2014}+1+\frac{x+2}{2013}+1+\frac{x+3}{2012}+1=0\)
\(\left(\frac{x+1}{2014}+\frac{2014}{2014}\right)+\left(\frac{x+2}{2013}+\frac{2013}{2013}\right)+\left(\frac{x+3}{2012}+\frac{2012}{2012}\right)=0\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)
\(\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\right)=0\)
Mà \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\ne0\)
\(\Rightarrow x+2015=0\)
\(\Rightarrow x=-2015\)
Vậy \(x=-2015\).
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\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)
\(\Rightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=0\)
\(\Rightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)
\(\Rightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\right)=0\)
Dễ thấy : \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\ne0\)
\(\Rightarrow x+2015=0\)
\(\Rightarrow x=-2015\)
Vậy \(x=-2015\)
\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)
\(\Leftrightarrow\frac{x+1}{2014}+1+\frac{x+2}{2013}+1+\frac{x+3}{2012}+1=0\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\ne0\right)=0\Leftrightarrow x=-2015\)
