Упростите выражение: (a^2/(a+b)-a^3/(a^2+2ab+b^2)*(1/ab+1/a^2).

Ответ:

\[\left( \frac{{a^{2}}^{\backslash a + b}}{a + b} - \frac{a^{3}}{a^{2} + 2ab + b^{2}} \right)\left( \frac{1^{\backslash a}}{\text{ab}} + \frac{1^{\backslash b}}{a^{2}} \right) =\]

\[= \frac{a^{3} + a^{2}b - a^{3}}{(a + b)^{2}} \cdot \frac{a + b}{a^{2}b} =\]

\[= \frac{a^{2}b(a + b)}{(a + b)^{2} \cdot a^{2}b} = \frac{1}{a + b}.\]