\(\dfrac{x+2}{x+3}-\dfrac{5}{\left(x+3\right)\left(x-2\right)}-\dfrac{2x}{x-2}=\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\dfrac{5}{\left(x+3\right)\left(x-2\right)}-\dfrac{2x\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-2\right)-5-2x\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=\dfrac{x^2-4-5-2x^2-6x}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{-x^2-6x-9}{\left(x+3\right)\left(x-2\right)}=\dfrac{-\left(x+3\right)^2}{\left(x+3\right)\left(x-2\right)}=\dfrac{-x-3}{x-2}\)
b.
\(\dfrac{x^2+5}{x^2+2x+1}+\dfrac{x-5}{x^2+2x+1}=\dfrac{x^2+x}{x^2+2x+1}=\dfrac{x\left(x+1\right)}{\left(x+1\right)^2}=\dfrac{x}{x+1}\)
