Simplify: $\;$ $\dfrac{\sqrt{a^2 - 2ab + b^2}}{\sqrt{a^2 + 2ab + b^2}} + \dfrac{2b}{a + b}$, $\;$ $0 < a < b$
$\dfrac{\sqrt{a^2 - 2ab + b^2}}{\sqrt{a^2 + 2ab + b^2}} + \dfrac{2b}{a + b}$
$= \dfrac{\sqrt{\left(a - b\right)^2}}{\sqrt{\left(a + b\right)^2}} + \dfrac{2b}{a + b}$
$= \dfrac{a - b}{a + b} + \dfrac{2b}{a + b}$
$= \dfrac{a + b}{a + b}$
$= 1$