\(\frac{x}{2x+4}+\frac{3x+2}{x^2-4}\)
= \(\frac{x}{2x+4}+\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
= \(\frac{x}{2x+4}+\frac{2}{x-1}\)
=\(\frac{x\left(x-1\right)+2\left(2x+4\right)}{\left(2x+4\right)\left(x-1\right)}\)
= \(\frac{x^2-x+4x+8}{2x^2-2x+4x-4}\)
= \(\frac{x^2+3x+8}{2x^2+2x-4}\)
\(\frac{x}{2x+4}+\frac{3x+2}{x^2-4}=\frac{x}{2\left(x+2\right)}+\frac{3x+2}{\left(x+2\right)\left(x-2\right)}=\frac{x\left(x-2\right)+\left(3x+2\right)2}{2\left(x+2\right)\left(x-2\right)}=\frac{x^2-2x+6x+4}{2\left(x-2\right)\left(x+2\right)}=\frac{x^2-4x+4}{2\left(x-2\right)\left(x+2\right)}=\frac{\left(x-2\right)^2}{2\left(x-2\right)\left(x+2\right)}=\frac{x-2}{2\left(x+2\right)}\)
