Question

giải phương trình sau

\(\frac{x-2}{98}+\frac{x-199}{99}=\frac{x}{100}+\frac{x-201}{101}\)

Answer 1

\(\frac{x-2}{98}+\frac{x-199}{99}=\frac{x}{100}+\frac{x-201}{101}\)

\(\frac{x-2}{98}-1+\frac{x-199}{99}+1=\frac{x}{100}-1+\frac{x-201}{101}+1\)

\(\frac{x-2-98}{98}+\frac{x-199+99}{99}=\frac{x-100}{100}+\frac{x-201+101}{101}\)

\(\frac{x-100}{98}+\frac{x-100}{99}=\frac{x-100}{100}+\frac{x-100}{101}\)

\(\frac{x-100}{98}+\frac{x-100}{99}-\frac{x-100}{100}-\frac{x-100}{101}=0\)

\(\left(x-100\right)\cdot\left(\frac{1}{98}+\frac{1}{99}-\frac{1}{100}-\frac{1}{101}\right)=0\)

⇒ x - 100 = 0 ⇒ x = 100

vậy x = 100