_____Giải phương trình sau______ $\frac{x-5}{100}$+ $\frac{x-4}{101}$+ $\frac{x-3}{102}$= $\frac{x-100}{5}$+ $\frac{x-101}{4}$ +$\frac{x-102}{3}$

Đáp án:

 x=150

Giải thích các bước giải:

$\frac{x-5}{100}$ +$\frac{x-4}{101}$ +$\frac{x-3}{102}$=$\frac{x-100}{5}$+ $\frac{x-101}{4}$+ $\frac{x-102}{3}$ 

⇔($\frac{x-5}{100}$-1)+( $\frac{x-4}{101y}$-1)+( $\frac{x-3}{102}$-1) =($\frac{x-100}{5}$-1)+( $\frac{x-101}{4}$-1)+( $\frac{x-102}{3}$-1)  

⇔$\frac{x-105}{100}$+ $\frac{x-105}{101}$+$\frac{x-105}{102}$ =$\frac{x-105}{5}$+ $\frac{x-105}{4}$+ $\frac{x-105}{3}$ 

⇔(x-150).($\frac{1}{100}$ +$\frac{1}{101}$+ $\frac{1}{102}$ – $\frac{1}{5}$ – $\frac{1}{4}$ -$\frac{1}{3}$ )=0

⇔x-150=0 (thấy ($\frac{1}{100}$ +$\frac{1}{101}$+ $\frac{1}{102}$ – $\frac{1}{5}$ – $\frac{1}{4}$ -$\frac{1}{3}$ $\neq$ 0)

⇒x=150

 vậy x=150