\(4,\dfrac{7x}{x-2}+\dfrac{14}{2-x}=\dfrac{7x}{x-2}-\dfrac{14}{x-2}=\dfrac{7x-14}{x-2}=\dfrac{7\left(x-2\right)}{x-2}=7\)
\(5,\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x^2+3x}=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}=\dfrac{x\left(x+1\right)}{2x\left(x+3\right)}+\dfrac{2\left(2x+3\right)}{2x\left(x+3\right)}=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
\(6,\dfrac{-3x+5}{2\left(5-x\right)}+\dfrac{x}{5-x}=\dfrac{5-3x}{2\left(5-x\right)}+\dfrac{2x}{2\left(5-x\right)}=\dfrac{5-3x+2x}{2\left(5-x\right)}=\dfrac{5-x}{2\left(5-x\right)}=\dfrac{1}{2}\)
