Question

$a^{3} + a^{2}b ÷ a^{2} +2ab+ b^{2}$

Answer 1

$\frac{a^3+a^2b}{a^2+2ab+b^2} = \frac{a^2(a+b)}{(a+b)^2}\\\\\ \frac{a^2(a+b)}{(a+b)(a+b)}\\\\\ \boxed{\frac{a^2}{(a+b)}}$

Answer 2

$a^{3} + a^{2}b ÷ a^{2} +2ab+ b^{2}$
    a³ + a²b      =     a² ( a + b )  ==>       a²     
 a² +2ab + b²       (a + b)(a + b)           a + b