Question : What value of $y$ will satisfy the following equation?
$\frac{3 y}{1+\frac{1}{1+\frac{y}{1–y}}} = 2$

Option 1: $\frac{2}{3}$

Option 2: $\frac{5}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{2}$

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

Question : If $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers), then what is the value of $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}$?

Option 1: –1

Option 2: –2

Option 3: 1

Option 4: 2

Question : If $2 x-y=2$ and $x y=\frac{3}{2}$, then what is the value of $x^3-\frac{y^3}{8}?$

Option 1: $\frac{9}{2}$

Option 2: $-\frac{5}{4}$

Option 3: $\frac{5}{2}$

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

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

Option 1: $\frac{5}{2}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{5}{4}$

Option 4: $\frac{3}{2}$

Question : If $x:y=3:2$, then the value of $\frac{x+y}{x–y}$ is:

Option 1: $5:1$

Option 2: $1:3$

Option 3: $1:5$

Option 4: $3:1$