Question : If $x=a^{\frac{1}{2}}+a^{-\frac{1}{2}}$, $y=a^{\frac{1}{2}}- a^{-\frac{1}{2}}$, then the value of $(x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$ is:

Option 1: 16

Option 2: 13

Option 3: 12

Option 4: 14

Question : The simplified value of $\small \left (1-\frac{2xy}{x^{2}+y^{2}}\right )\div\left (\frac{x^{3}-y^{3}}{x-y}-3xy\right)$ is:

Option 1: $\frac{1}{x^{2}-y^{3}}$

Option 2: $\frac{1}{x^{2}+y^{2}}$

Option 3: $\frac{1}{x-y}$

Option 4: $\frac{1}{x+y}$

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$