Question

Tìm giá trị của x biết: \(\frac{x+5}{100}+\frac{x+5}{99}=\frac{x+5}{98}+\frac{x+5}{97}\)

HELP ME (mk đang cần gấp)

Answer 1

\(\frac{x+5}{100}+\frac{x+5}{99}=\frac{x+5}{98}+\frac{x+5}{97}\)

\(\Leftrightarrow\frac{x+5}{100}+\frac{x+5}{99}-\frac{x+5}{98}-\frac{x+5}{97}=0\)

\(\Leftrightarrow\left(x+5\right)\left(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\right)=0\)

\(\Leftrightarrow x+5=0\) (Vì: \(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\ne0\) )

\(\Leftrightarrow x=-5\)

Answer 2

\(\frac{x+5}{100}+\frac{x+5}{99}=\frac{x+5}{98}+\frac{x+5}{97}\)

\(\Rightarrow\frac{x+5}{100}+\frac{x+5}{99}-\frac{x+5}{98}-\frac{x+5}{97}=0\)

\(\Rightarrow\left(x+5\right)\left(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\right)=0\)

Mà \(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\ne0\)

\(\Rightarrow x+5=0\)

\(\Rightarrow x=-5\)

Vậy \(x=-5\)