Question : What is the value of $\frac{1+\mathrm{x}}{1-\mathrm{x}^2} \div \frac{1+\mathrm{x}}{1-\mathrm{x}^4}-\frac{1-\mathrm{x}^4}{1-\mathrm{x}} \times \frac{1+\mathrm{x}}{1-\mathrm{x}^2}$?

Option 1: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(1-\mathrm{x})}$

Option 2: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(\mathrm{x}-1)}$

Option 3: $(1-\mathrm{x})^2$

Option 4: $\left(1+\mathrm{x}^2\right)$

Question : If $\mathrm{m}-\frac{1}{\mathrm{~m}}=7$, then what is the value of $\mathrm{m}^2+\frac{1}{\mathrm{~m}^2}$?

Option 1: 0

Option 2: 51

Option 3: 53

Option 4: 49

Question : If $x+\frac{1}{x}=\mathrm{\frac{K}{2}}$, then what is the value of $\frac{x^8+1}{x^4} ?$

Option 1: $\frac{\mathrm{K}^4-16 \mathrm{~K}^2+32}{16}$

Option 2: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-36}{32}$

Option 3: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-32}{16}$

Option 4: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2+32}{16}$

Question : If $x+\frac{2}{x}=1$, then the value of $\frac{x^2+7x+2}{x^2+13x+2}$ is:

Option 1: $\frac{5}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{2}{7}$

Question : If $\frac{x}{y}=\frac{4}{5}$, then the value of $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is:

Option 1: $\frac{3}{7}$

Option 2: $1\frac{1}{7}$

Option 3: $1$

Option 4: $2$