The equation $\sqrt{(\mathrm{x}-1)}-\sqrt{(\mathrm{x}-1)}=\sqrt{(4\mathrm{x}-1)}$ has

Given $\sqrt{(\mathrm{x}+1)}-\sqrt{(\mathrm{x}-1)}=\sqrt{(4\mathrm{x}-1)}$

Squaring both sides, we get $-2\sqrt{({\mathrm{x}}^2-1)} =2\mathrm{x}-1$

Squaring again, we get $\mathrm{x}=5/4$ which does not satisfy the given equation. Hence equation has no solution.