If $\dfrac{x^2 - 1}{x^2 + 1} =\dfrac{3}{5}$, the value of x is :

1. $\dfrac{1}{2}$

2. 2

3. $\pm \dfrac{1}{2}$

4. $\pm 2$

Given,

$\Rightarrow \dfrac{x^2 - 1}{x^2 + 1} =\dfrac{3}{5} \\[1em] \Rightarrow 5(x^2 - 1) = 3(x^2 + 1) \\[1em] \Rightarrow 5x^2 - 5 = 3x^2 + 3 \\[1em] \Rightarrow 5x^2 - 3x^2 = 3 + 5 \\[1em] \Rightarrow 2x^2 = 8 \\[1em] \Rightarrow x^2 = 4 \\[1em] \Rightarrow x = \sqrt{4} \\[1em] \Rightarrow x = \pm 2.$

Hence, Option 4 is the correct option.