a: |x-5|=|2x-10|
=>2|x-5|-|x-5|=0
=>|x-5|=0
=>x-5=0
=>x=5
b: \(\left|x-3\right|=2x+2\)
=>\(\left\{{}\begin{matrix}2x+2>=0\\\left(2x+2\right)^2=\left(x-3\right)^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-1\\\left(2x+2+x-3\right)\left(2x+2-x+3\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=-1\\\left(3x-1\right)\left(x+5\right)=0\end{matrix}\right.\Leftrightarrow x=\dfrac{1}{3}\)
c:
ĐKXĐ: \(x\notin\left\{1;-2\right\}\)
\(\dfrac{3}{x+2}+\dfrac{1}{x-1}=\dfrac{5}{\left(x+2\right)\left(x-1\right)}\)
=>\(\dfrac{3\left(x-1\right)+x+2}{\left(x+2\right)\left(x-1\right)}=\dfrac{5}{\left(x+2\right)\left(x-1\right)}\)
=>3x-3+x+2=5
=>4x-1=5
=>4x=6
=>\(x=\dfrac{3}{2}\left(nhận\right)\)