If x + 1/x = √13, then 3x/($$x^{2}$$-1) equal to

Given : $$x+\frac{1}{x}=\sqrt{13}$$

Squaring both sides

=> $$(x+\frac{1}{x})^2=(\sqrt{13})^2$$

=> $$x^2+\frac{1}{x^2}+(2.x.\frac{1}{x})=13$$

=> $$x^2+\frac{1}{x^2}=13-2=11$$ ------------(i)

Also, we know that : $$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-(2.x.\frac{1}{x})$$

Substituting value from equation (i)

=> $$(x-\frac{1}{x})^2=11-2=9$$

=> $$(x-\frac{1}{x})=\sqrt{9}=3$$

=> $$x^2-1=3x$$

=> $$\frac{3x}{x^2-1}=1$$

=> Ans - (C)