In △ ABC, DE // BC, AD = a, DB = b and BC = x, then, DE is equal to :

1. $\dfrac{a + b}{ax}$

2. $\dfrac{a + b}{a}$

3. $\dfrac{ax}{a + b}$

4. $\dfrac{a}{a + b}$

In △ ADE and △ ABC,

⇒ ∠DAE = ∠BAC (Common angles)

⇒ ∠ADE = ∠ABC (Corresponding angles are equal)

∴ △ ADE ~ △ ABC (By A.A. axiom)

We know that,

Corresponding sides of similar triangles are proportional.

$\Rightarrow \dfrac{AD}{AB} = \dfrac{DE}{BC} \\[1em] \Rightarrow \dfrac{a}{a + b} = \dfrac{DE}{x} \\[1em] \Rightarrow DE = \dfrac{ax}{a + b}.$

Hence, Option 3 is the correct option.