Answer:
[tex]\frac{x+1}{x^{2} +2x}[/tex]
Step-by-step explanation:
A good first step in tackling this problem is to factor out any polynomials so combining the two terms becomes easy
[tex]\frac{-2}{x^2-4}+\frac{x-1}{x^{2} -2x}\\\frac{-2}{(x-2)(x+2)}+\frac{x-1}{x(x-2)}\\[/tex]
in the first term the denominator is missing a factor of x and in the second term the denominator is missing a factor of x+2
so
[tex]\frac{-2x}{x(x-2)(x+2)}+\frac{(x+2)(x-1)}{x(x-2)(x+2)}\\[/tex]
now simply add
[tex]\frac{-2x+(x+2)(x-1)}{x(x-2)(x+2)}\\\\\frac{-2x+x^{2}+x-2 }{x(x-2)(x+2)}\\\\\frac{x^{2}-x-2 }{x(x-2)(x+2)}\\\\\frac{(x-2)(x+1) }{x(x-2)(x+2)}[/tex]
Finally cancel common factors
[tex]\frac{(x+1) }{x(x+2)}\\\\\frac{x+1 }{x^{2} +2x}\\[/tex]
