Question

[nguyễn thị thảo vy]

giải pt:

\(\frac{x-5}{1990}\)+\(\frac{x-15}{1980}\)=\(\frac{x-1980}{15}\)+\(\frac{x-1990}{5}\)

Answer 1

[Nguyễn Xuân Anh]

\(\frac{x-5}{1990}-1+\frac{x-15}{1980}-1=\frac{x-1980}{15}-1+\frac{x-1990}{5}-1\)

\(\frac{x-1995}{1990}+\frac{x-1995}{1980}-\frac{x-1995}{15}-\frac{x-1995}{5}=0\)

\(\left(x-1995\right)\left(\frac{1}{1990}+\frac{1}{1980}-\frac{1}{15}-\frac{1}{5}\right)=0\)

Mà \(\frac{1}{1990}+\frac{1}{1980}-\frac{1}{15}-\frac{1}{5}\ne0\)

Nên \(x-1995=0\Leftrightarrow x=1995\)