If $\mathrm{x}=\frac{2\mathrm{ab}}{\mathrm{a}+\mathrm{b}}$, find the value of $\frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}-\mathrm{a}}+\frac{\mathrm{x}+\mathrm{b}}{\mathrm{x}-\mathrm{b}}$.

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{2-x}+\sqrt{2+x}}{\sqrt{2-x}-\sqrt{2+x}}=3$

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{\mathrm{x}+4}+\sqrt{\mathrm{x}-10}}{\sqrt{\mathrm{x}+4}-\sqrt{\mathrm{x}-10}}=\frac{5}{2}$

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}=\frac{a}{b}$

Using properties of proportion, find $\mathrm{x}$ from the following equations:

$\frac{\sqrt{5\mathrm{x}}+\sqrt{2\mathrm{x}-6}}{\sqrt{5\mathrm{x}}-\sqrt{2\mathrm{x}-6}}=4$.

Using properties of proportion, find $x$ from the following equations:

$\frac{\sqrt{a+x}+\sqrt{a-x}}{\sqrt{a+x}-\sqrt{a-x}}=\frac{c}{d}$

Using properties of proportion, find $x$ from the following equations:

$\frac{\mathrm{a}+\sqrt{{\mathrm{a}}^2-2\mathrm{ax}}}{\mathrm{a}-\sqrt{{\mathrm{a}}^2-2\mathrm{ax}}}=\mathrm{b}$.