1/
\(\dfrac{2}{x+3}+\dfrac{1}{x}\\ =\dfrac{2x}{x\cdot\left(x+3\right)}+\dfrac{x+3}{x\cdot\left(x+3\right)}\\ =\dfrac{2x+x+3}{x\cdot\left(x+3\right)}=\dfrac{3x+3}{x\cdot\left(x+3\right)}\)
4/
\(\dfrac{6-x}{x^2+3x}+\dfrac{3}{2x+6}\\ =\dfrac{6-x}{x\cdot\left(x+3\right)}+\dfrac{3}{2\cdot\left(x+3\right)}\\ =\dfrac{2\cdot\left(6-x\right)}{2x\cdot\left(x+3\right)}+\dfrac{3x}{2x\cdot\left(x+3\right)}=\dfrac{12-2x+3x}{2x\cdot\left(x+3\right)}\\ =\dfrac{12+x}{2x\cdot\left(x+3\right)}\)
7/
\(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\\ =\dfrac{1}{x\cdot\left(y-x\right)}-\dfrac{1}{y\cdot\left(y-x\right)}\\ =\dfrac{y}{xy\cdot\left(y-x\right)}-\dfrac{x}{xy\cdot\left(y-x\right)}=\dfrac{y-x}{xy\cdot\left(y-x\right)}=\dfrac{1}{xy}\)
