Question : Simplify the given expression.
$(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)$

Option 1: $2y(x - 3y)$

Option 2: $2y(x + 3y)$

Option 3: $2x(x - 3y)$

Option 4: $2x(x + 3y)$

Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}$, where $x \neq y \neq z$, is:

Option 1: $0$

Option 2: $\frac{1}{(x+y+z)}$

Option 3: $\frac{1}{(x+y)(y+z)(z+x)}$

Option 4: $1$

Question : What is $\frac{\left (x^{2}-y^{2} \right)^{3}+\left (y^{2}-z^{2} \right )^{3}+\left (z^{2}-x^{2} \right )^{3}}{\left (x-y \right)^{3}+\left (y-z \right )^{3}+\left (z-x \right)^{3}}?$

Option 1: $\frac{(x+y)(y+z)}{(x+z)}$

Option 2: $(x+y)^3(y+z)^3(z+x)^3$

Option 3: $(x+y)(y+z)(z+x)$

Option 4: $(x+y)(y+z)$

Question : If $\frac{x^{2}-x+1}{x^{2}+x+1}=\frac{2}{3}$, then the value of $\left (x+\frac{1}{x} \right)$ is:

Option 1: 4

Option 2: 5

Option 3: 6

Option 4: 8

Question : What is the simplified value of
$\left(1-\frac{1}{4-\frac{2}{1+\frac{1}{\frac{1}{3}+2}}}\right) \times \frac{15}{16} \div \frac{2}{3}$ of $2 \frac{1}{4}-\frac{3+4}{3^3+4^3}$

Option 1: $\frac{5}{13}$

Option 2: $\frac{4}{13}$

Option 3: $\frac{8}{13}$

Option 4: $\frac{6}{13}$