\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Mà \(\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)\ne0\)
\(\Rightarrow x+1=0\)
\(\Leftrightarrow x=0-1\)
\(\Leftrightarrow x=-1\)
Vậy \(x=-1\)
x+1/10 + x+1/11 + x+1/12 = x+1/13 + x+1/14 = 0
<=> x+1/10 + x+1/11 + x+1/12 - x+1/13 - x+1/14 = 0
<=> (x+1)(1/10 + 1/11 + 1/12 - 1/13 - 1/14) = 0
Mà (1/10 + 1/11+ 1/12 - 1/13 - 1/14) khác 0
=> x+1 = 0
<=> x = 0-1
<=> x = -1
Vậy x = -1