wenn ich mich so spät abends nicht vertippe:
\(\displaystyle \frac{a}{a b-b^{2}}-\frac{b}{a^{2}+a b}-\frac{1}{a+b}+\frac{1}{a} \)
\(\displaystyle = \frac{a}{b(a-b)}-\frac{b}{a(a+ b)}-\frac{1}{a+b}+\frac{1}{a} \)
\(\displaystyle = \frac{a^2 (a+b) -b^2(a-b)-ab(a-b)+b(a+b)(a-b) }{ab(a+b)(a-b)} \)
\(\displaystyle = \frac{a^3 +a^2b -ab^2+b^3-a^2b+ab^2+a^2b-ab^2+ab^2-b^3}{ab(a+b)(a-b)} \)
\(\displaystyle = \frac{a^3 +a^2b}{ab(a+b)(a-b)}=\frac{a(a^2+ab)}{(a^2+ab)(ab-b^2)} \)
\(\displaystyle = \frac{a}{ab-b^2} \)