Question

tìm x

\(\dfrac{x-11}{101}-\dfrac{x-13}{103}=\dfrac{x-17}{107}-\dfrac{x-19}{109}\)

Answer 1

\(\dfrac{x-1}{101}-\dfrac{x-13}{103}=\dfrac{x-17}{107}-\dfrac{x-19}{109}\)

\(\Rightarrow\left(\dfrac{x-11}{101}+1\right)-\left(\dfrac{x-13}{103}+1\right)=\left(\dfrac{x-17}{107}+1\right)-\left(\dfrac{x-19}{109}+1\right)\)

\(\Rightarrow\dfrac{x+90}{101}-\dfrac{x+90}{103}=\dfrac{x+90}{107}-\dfrac{x+90}{109}\)

\(\Rightarrow\dfrac{x+90}{101}-\dfrac{x+90}{103}-\dfrac{x+90}{107}+\dfrac{x+90}{109}=0\)

\(\Rightarrow\left(x+90\right)\left(\dfrac{1}{101}-\dfrac{1}{103}-\dfrac{1}{107}+\dfrac{1}{109}\right)=0\)

Vì \(\dfrac{1}{101}-\dfrac{1}{103}-\dfrac{1}{107}+\dfrac{1}{109}\ne0\)

Nên \(x+90=0\Rightarrow x=-90\)