$\dfrac{x+1}{13}+$$\dfrac{x+2}{12}=$$\dfrac{x+3}{11}+$$\dfrac{x+4}{10}$

$\dfrac{x+1}{13}+1$$\dfrac{x+2}{12}+1=$$\dfrac{x+3}{11}+1$$\dfrac{x+4}{10}+1$

$\dfrac{x+14}{13}+$$\dfrac{x+14}{12}=$$\dfrac{x+14}{11}+$$\dfrac{x+14}{10}$

$\dfrac{x+14}{13}+$$\dfrac{x+14}{12}-\dfrac{x+14}{11}-$$\dfrac{x+14}{10}=0$

$\text{(x+14)}$($\dfrac{1}{13}+$$\dfrac{1}{12}-$$\dfrac{1}{11}-$$\dfrac{1}{10})=0$

$\text{Vì }$ ($\dfrac{1}{13}+$$\dfrac{1}{12}-$$\dfrac{1}{11}-$$\dfrac{1}{10}) > 0$ $\text{mà }$ $\text{(x+14)}$($\dfrac{1}{13}+$$\dfrac{1}{12}-$$\dfrac{1}{11}-$$\dfrac{1}{10})=0$

⇒ $\text{(x+14)}=0$

⇒ $\text{x = -14}$

`(x+1)/13+(x+2)/12=(x+3)/11+(x+4)/10`

`⇔ ((x+1)/13+1)+((x+2)/12+1)=((x+3)/11+1)+((x+4)/10+1)`

`⇔ (x+14)/13+(x+14)/12=(x+14)/11+(x+14)/10`

`⇔ (x+14)/13+(x+14)/12-((x+14)/11+(x+14)/10)=0`

`⇔ (x+14)/13+(x+14)/12-(x+14)/11-(x+14)/10=0`

`⇔ (x+14).(1/13+1/12-1/11-1/10)=0`

Vì `1/13+1/12-1/11-1/10 \ne 0 ⇒` Ta có :

`x+14=0`

`⇔ x=0-14`

`⇔ x=-14`

Vậy `x=-14`