Verified answer

1. 2/(x¹/⁴-y¹/⁴)+2/(x¹/⁴+y¹/⁴)=(2*(x¹/⁴+y¹/⁴)+2*(x¹/⁴-y¹/⁴)/(x¹/²-y¹/²)=

=(2*x¹/⁴+2*y¹/⁴+2*x¹/⁴-2*y¹/⁴)/(x¹/²-y¹/²)=(4*x¹/⁴)/(x¹/²-y¹/²).

2. x⁻¹/²-y⁻¹/²=1/x¹/²-1/y¹/²=(y¹/²-x¹/²)/(x⁻¹/²*y⁻¹/²)=(y¹/²-x¹/²)*(x¹/²*y¹/²).

3. ((y¹/²-x¹/²)/(x¹/²*y¹/²))*((x¹/⁴*y¹/²)/6))=

=-(x¹/²-y¹/²)*(x¹/⁴*y¹/²)/(6*(x¹/²*y¹/²))=-(x¹/²-y¹/²)*(6*x¹/⁴).

4. ((4*x¹/⁴)/(x¹/²-y¹/²))/(-(x¹/²-y¹/²)*(6*x¹/⁴)=-(4*x¹/⁴)/(6*x¹/⁴)=-2/3.