<s>[INST] Evaluate $\frac{2a}{a^2-4} - \frac{1}{a-2}-\frac{1}{a^2+2a}$ 
Evaluate
$$\dfrac{2a}{a^2-4} - \dfrac{1}{a-2}-\dfrac{1}{a^2+2a}$$

We have to see what their common term is. Therefrom, we can evaluate the simplified expression by canceling out.
$$a^2 - 4 = (a)^2 - (2)^2  = (a-2)(a+2) \tag {1}$$
$$a^2 +2a = a(a+2)\tag{2}$$
Rewriting the expression
$$\dfrac{2a}{(a-2)(a+2)} - \dfrac{1}{a-2}-\dfrac{1}{a(a+2)}$$
$$\dfrac{2a}{(a-2)(a+2)} - \dfrac{(a+2)}{(a-2)(a+2)}-\dfrac{1}{a(a+2)}$$
Factoring $\dfrac{1}{a+2}$
$$\dfrac{1}{a+2}\biggr (\dfrac{2a}{a-2} - \dfrac{a+2}{a-2}-\dfrac{1}{a}\biggr )$$
This is where I'm stuck. Could you assist me?
Regards
 [/INST] Hint: You can write $$\frac{2a^2}{a(a-2)(a+2)}-\frac{a(a+2)}{a(a-2)(a+2)}-\frac{a-2}{a(a+2)(a-2)}$$
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