Nghiệm của phương trình x-3/100+x-2/102+x-1/103=x-101/3+x-102/2+x-103

* Hướng dẫn giải

$$\begin{gathered} \frac{x-3}{101}+\frac{x-2}{102}+\frac{x-1}{103}=\frac{x-101}{3}+\frac{x-102}{2}+x-103 \\ \iff \left(\frac{x-3}{101}-1\right)+\left(\frac{x-2}{102}-1\right)+\left(\frac{x-1}{103}-1\right)=\left(\frac{x-101}{3}-1\right)+\left(\frac{x-102}{2}-1\right)+x-104 \\ \iff \frac{x-104}{101}+\frac{x-104}{102}+\frac{x-104}{103}=\frac{x-104}{3}+\frac{x-104}{2}+x-104 \\ \iff \left(x-104\right)\left(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}-\frac{1}{3}-\frac{1}{2}-1\right)=0 \\ \iff x=104 \end{gathered}$$