The equation $\sqrt{x+1}-\sqrt{x-1}= \sqrt{4x-1}$ has

no solution

We have,

$\sqrt{x+1}-\sqrt{x-1}= \sqrt{4x-1}$  ...(i)

$⇒(\sqrt{x+1}-\sqrt{x-1})^2=(\sqrt{4x-1})^2$

$⇒x+1+x-1-2\sqrt{x^2-1}=4x-1$

$⇒2x-2\sqrt{x^2-1}=4x-1$

$⇒-2\sqrt{x^2-1}=2x-1$

$⇒4(x^2-1)=(2x-1)^2$

$⇒4x^2-4=4x^2-4x+1⇒x=5/4$

But, $x=\frac{5}{4}$ does not satisfy equation (i).

Hence, equation (i) has no solution.