Evaluate $\frac{0.53 \times 0.53 - 2 \times 0.53 \times 0.41 + 0.41 \times 0.41}{0.53 - 0.41}$

If we multiply a fraction by itself and divide the product by its reciprocal,the fraction thus obtained is $18 \frac{26}{27}$. The original fraction is

If $\sqrt{1+\frac{x}{144}}=\frac{13}{12},$ then $x$ equals to

The value of $4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}$ is:

If $x = \frac{4 \sqrt{ab}}{\sqrt{a} + \sqrt{b}}$,then what is the value of $\frac{x + 2 \sqrt{a}}{x - 2 \sqrt{a}} + \frac{x + 2 \sqrt{b}}{x - 2 \sqrt{b}}$ (when $a \neq b$)?

Simplify:
$\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+\sqrt{a}}$