b)
[tex]\frac{x-5}{x}-\frac{x}{x+2}=\frac{(x-5)(x+2)}{x(x+2)}-\frac{x^2}{x(x+2)}=\frac{x^2+2x-5x-10-x^2}{x(x+2)}=\frac{-3x-10}{x(x+2)}=-\frac{3x+10}{x(x+2)}[/tex]
c)
[tex]\frac{2}{x}+\frac{2}{x+3}=\frac{2(x+3)}{x(x+3)}+\frac{2x}{x(x+3)}=\frac{2x+6+2x}{x(x+3)}=\frac{4x+6}{x(x+3)}[/tex]
d)
[tex]\frac{x+6}{x^2-9}+\frac{-2}{x+3}=\frac{x+6}{(x-3)(x+3)}+\frac{-2(x-3)}{(x-3)(x+3)}=\frac{x+6-2x+6}{(x-3)(x+3)}=\frac{-x+12}{(x-3)(x+3)}[/tex]