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\(\frac{x-4}{2015}-\frac{1}{2015}=\frac{10-2x}{2015}\)
\(\Rightarrow\frac{x-4}{2015}-\frac{10-2x}{2015}=\frac{1}{2015}\)
\(\Rightarrow\frac{x-4-\left(10-2x\right)}{2015}=\frac{1}{2015}\)
\(\Rightarrow\frac{\left(x+2x\right)-\left(4+10\right)}{2015}=\frac{1}{2015}\)
\(\Rightarrow\frac{3x-14}{2015}=\frac{1}{2015}\)
\(\Rightarrow\left(3x-14\right).2015=2015\)
\(\Rightarrow3x-14=1\) ( bớt cả 2 vế đi 2015 lần )
\(\Rightarrow3x=15\)
\(\Rightarrow x=5\)
Vậy \(x=5\)
\(\frac{x+2015}{x-2015}=\frac{y+2017}{y-2017}\)
\(\frac{x+2015}{y+2017}=\frac{x-2015}{y-2017}\)
Áp dụng tính chất của dãy tỉ số bằng nhau,ta có :
\(\frac{x+2015}{y+2017}=\frac{x-2015}{y-2017}=\frac{\left(x+2015\right)-\left(x-2015\right)}{\left(y+2017\right)-\left(y-2017\right)}=\frac{2015}{2017}\)( 1 )
\(\frac{x+2015}{y+2017}=\frac{x-2015}{y-2017}=\frac{\left(x+2015\right)+\left(x-2015\right)}{\left(y+2017\right)+\left(y-2017\right)}=\frac{x}{y}\)( 2 )
Từ ( 1 ) và ( 2 ) \(\Rightarrow\frac{x}{y}=\frac{2015}{2017}\)
\(\frac{x-1}{2015}-\frac{1}{2015}=\frac{10-2x}{2015}\)
\(\Rightarrow x-1-1=10-2x\)
\(\Rightarrow x-2=10-2x\)
\(\Rightarrow-2x+x=10+2\)
\(\Rightarrow-x=12\Rightarrow x=-12\)
\(\frac{x+2015}{2016}+\frac{x+2016}{2015}+\frac{x+2017}{2014}=-3\)
\(\Leftrightarrow\frac{x+2015}{2016}+1+\frac{x+2016}{2015}+1+\frac{x+2017}{2014}+1=0\)
\(\Leftrightarrow\frac{x+4031}{2016}+\frac{x+4031}{2015}+\frac{x+4031}{2014}=0\)
\(\Leftrightarrow\left(x+4031\right)\left(\frac{1}{2016}+\frac{1}{2015}+\frac{1}{2014}\right)=0\)
Có: \(\frac{1}{2016}+\frac{1}{2015}+\frac{1}{2014}\ne0\)
\(\Rightarrow x+4031=0\)
\(\Rightarrow x=-4031\)