Tìm x, biết (x+4)/2014+(x_3)/2015=(x+2)/2016+(x+1)/2017

a) \(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}=\dfrac{x+1}{13}+\dfrac{x+1}{14}\)

\(\Rightarrow6006\left(x+1\right)+5460\left(x+1\right)+5005\left(x+1\right)=4620\left(x+1\right)+4290\left(x+1\right)\)

\(\Leftrightarrow\left(6006+5460+5005\right)\cdot\left(x+1\right)=\left(4620+4290\right)\cdot\left(x+1\right)\)

\(\Leftrightarrow16471\left(x+1\right)=8910\left(x+1\right)\)

\(\Leftrightarrow16471x+16471=8910x+8910\)

\(\Leftrightarrow16471x-8910x=8910-16471\)

\(\Leftrightarrow7561x=-7561\)

\(\Rightarrow x=-1\)

Vậy \(x=-1\)

b) \(\dfrac{x+4}{2014}+\dfrac{x+3}{2015}=\dfrac{x+2}{2016}+\dfrac{x+1}{2017}\)

\(\Rightarrow4096749040\left(x+4\right)+4094735904\left(x+3\right)=4092704785\left(x+2\right)+4090675680\left(x+1\right)\)

\(\Leftrightarrow4096769040x+16387076160+4094735904x+12284207712=4092704785x+8185409570+4090675680x+4090675680\)

\(\Leftrightarrow8191504944x+28671283872=8183380465x+12276085250\)

\(\Leftrightarrow8191504944x-8183380465x=12276085250-28671283872\)

\(\Leftrightarrow8124479x=-16395198622\)

\(\Rightarrow x=-2018\)

Vậy \(x=-2017\)

P/s: đây không phải cách làm tối ưu, vì vậy mình nghĩ bạn nên tham khảo từ các bài làm khác nhé!