The sum of an irrational number and its rationalising factor is always

When we Rationalise the denominator of $\frac{1}{2\sqrt{5}-\sqrt{3}}$ we get $\frac{a+b}{c}$. Find the value of $c$

When rationalise the denominator of $\frac{3}{5-\sqrt{3}}+\frac{2}{5+\sqrt{3}}$ we get $\frac{a+b}{c}$. Find the value of $a$

When we Rationalise the denominator of  $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ we get $a+b$. Find the value of $a$

When we simplify $\sqrt{112}-\sqrt{63}+\frac{224}{\sqrt{28}}$ we get $a\times \sqrt{b}$. Find the value of $a$.

When rationalise$\frac{2}{\sqrt{5}+\sqrt{3}}$ we get $\frac{a}{b}$. Find the value of $b$

When we simplify $\sqrt{\frac{5}{12}}$ we get $\frac{a}{b}$. Find the value of $b$.

If the rationalised form of $\frac{1}{4-\sqrt{3}}$ is of the form $\frac{a+\sqrt{3}}{b}$, then find the value of $\left(a+b\right)$.

When we rationalise $\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$ we get $\frac{a}{b}$. Find the value of $a$.

If the rationalised form of $\frac{1}{\sqrt{7}-\sqrt{6}}$ is in the form $\sqrt{a}+\sqrt{b}$ then, write the value of $\left(a+b\right)$ as final answer.

If the simplified form of $\sqrt{1\frac{46}{75}}$ is of the form $\frac{a\sqrt{3}}{b}$, then find the value of $\left(a+b\right)$.

Simplify:

$\frac{4\sqrt{18}}{\sqrt{12}}-\frac{8\sqrt{75}}{\sqrt{32}}+\frac{9\sqrt{2}}{\sqrt{3}}$