Question

Giải phương trình:

a)\(\dfrac{x-5}{100}+\dfrac{x-4}{101}=\dfrac{x-100}{5}+\dfrac{x-101}{4}\)

Answer 1

\(\dfrac{x-5}{100}+\dfrac{x-4}{101}=\dfrac{x-100}{5}+\dfrac{x-101}{4}\)

\(\Leftrightarrow\dfrac{x-5}{100}-1+\dfrac{x-4}{101}-1=\dfrac{x-100}{5}-1+\dfrac{x-101}{4}-1\)

\(\Leftrightarrow\dfrac{x-105}{100}+\dfrac{x-105}{101}-\dfrac{x-105}{5}-\dfrac{x-105}{4}=0\)

\(\Leftrightarrow\left(x-105\right)\left(\dfrac{1}{100}+\dfrac{1}{101}-\dfrac{1}{5}-\dfrac{1}{4}\right)=0\Leftrightarrow x=105\)