Question

a) x+2/x-2-1/x=2/x*(x-2)

b)2/2x-6+2/2x+2+2x/(x+1)*(3-x)=0

c) x+1/2017+x+2/2016=x+3/2015+x+4/2014

d) x-45/5+x-44/6+x-43/7+x-42/8=4

e) x-3/2011+x+2/2012=x-2012/2+x-2011/3

Answer 1

a) ĐKXĐ: \(x\notin\left\{0;2\right\}\)

Ta có: \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{x-2}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)

Suy ra: \(x^2+2x-x+2-2=0\)

\(\Leftrightarrow x^2+x=0\)

\(\Leftrightarrow x\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-1\left(nhận\right)\end{matrix}\right.\)

Vậy: S={-1}