a: 5x-10=0
=>5x=10
=>\(x=\dfrac{10}{5}=2\)
b: 4x+6=3x-15
=>4x-3x=-15-6
=>x=-21
c: \(4x^2-x=0\)
=>\(x\left(4x-1\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\4x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{4}\end{matrix}\right.\)
d: \(x\left(x+1\right)-\left(x+2\right)\left(x-3\right)=7\)
=>\(x^2+x-\left(x^2-x-6\right)=7\)
=>2x+6=7
=>2x=1
=>\(x=\dfrac{1}{2}\)
e: ĐKXĐ: \(x\notin\left\{2;-1\right\}\)
\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)
=>\(\dfrac{2\left(x-2\right)-x-1}{\left(x-2\right)\left(x+1\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)
=>3x-11=2x-4-x-1
=>3x-11=x-5
=>2x=6
=>x=3(nhận)
f: ĐKXĐ: \(x\notin\left\{0;2\right\}\)
\(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
=>\(\dfrac{x\left(x+2\right)-x+2}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)
=>\(x^2+2x-x+2=2\)
=>\(x^2+x=0\)
=>x(x+1)=0
=>\(\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-1\left(nhận\right)\end{matrix}\right.\)
