Question

Bài 1 : Tìm x

1) \(\frac{x-1}{10}\) +  \(\frac{x-1}{11}\)+\(\frac{x-1}{12}\)-\(\frac{x-1}{13}\)= 0

2 ) \(\frac{x-1}{99}\)+\(\frac{x-2}{98}\)+\(\frac{x-5}{95}\)= 3 + \(\frac{1}{99}\)+\(\frac{1}{98}\)+\(\frac{1}{95}\)

 

Answer 1

1) \(\left(x-1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}\right)=0\)

mà \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}\ne0\)

\(\Rightarrow x-1=0\Leftrightarrow x=1\)

2) \(\frac{x-1}{99}-1+\frac{x-2}{98}-1+\frac{x-5}{95}-1=\frac{1}{99}+\frac{1}{98}+\frac{1}{95}\)

\(\frac{x-100}{99}+\frac{x-100}{98}+\frac{x-100}{95}=\frac{1}{99}+\frac{1}{98}+\frac{1}{95}\)

\(\left(x-100\right)\left(\frac{1}{99}+\frac{1}{98}+\frac{1}{95}\right)=\frac{1}{99}+\frac{1}{98}+\frac{1}{95}\)

x - 100 = 1

x = 101