Question : Simplify the following expression.
$\frac{x^2-2 x-63}{x^2+14 x+49}$

Option 1: $\frac{x+9}{x+7}$

Option 2: $\frac{x-7}{x+7}$

Option 3: $\frac{x+7}{x-7}$

Option 4: $\frac{x-9}{x+7}$

Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:

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

Option 2: $\frac{1}{4}$

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

Option 4: $\frac{1}{5}$

Question : If $\frac{1}{x}+x=4$, then find $\frac{1}{x^2}+x^2$.

Option 1: 14

Option 2: 5

Option 3: 7

Option 4: 15

Question : If $x=\sqrt[3]{x^{2}+11} –2$, then the value of $(x^3+5x^2+12x)$ is:

Option 1: 0

Option 2: 3

Option 3: 7

Option 4: 11

Question : If $x+\frac{1}{x}=17,$ what is the value of $\frac{x^{4}+\frac{1}{x^{2}}}{x^{2}-3x+1}\; ?$

Option 1: $\frac{2431}{7}$

Option 2: $\frac{3375}{7}$

Option 3: $\frac{3375}{14}$

Option 4: $\frac{3985}{9}$