7.
ĐKXĐ: \(x\ne\left\{0;2\right\}\)
\(\Leftrightarrow\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{x-2}{x\left(x-2\right)}-\dfrac{2}{x\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{x\left(x+2\right)-\left(x-2\right)-2}{x\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{x^2-3x}{x\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{x\left(x-3\right)}{x\left(x-2\right)}=0\)
\(\Rightarrow\dfrac{x-3}{x-2}=0\)
\(\Rightarrow x-3=0\)
\(\Rightarrow x=3\) (thỏa mãn)
10.
ĐKXĐ: \(x\ge\left\{-3;2\right\}\)
\(\Leftrightarrow\dfrac{12\left(x-2\right)}{2\left(x-2\right)\left(x+3\right)}-\dfrac{2\left(x+3\right)}{2\left(x-2\right)\left(x+3\right)}-\dfrac{5\left(x-2\right)}{2\left(x-2\right)\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{12\left(x-2\right)-2\left(x+3\right)-5\left(x-2\right)}{2\left(x-2\right)\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{5x-20}{2\left(x-2\right)\left(x+3\right)}=0\)
\(\Rightarrow5x-20=0\)
\(\Rightarrow x=4\) (thỏa mãn)
