Q:

Fractions with 3 diffferent variables

Calculate the values of $a$, $b$ and $c$ if: $$\frac{5}{13} = \frac{1}{a+\frac{1}{b+\frac{2}{c}}}$$
Can anyone give me a hint and not the answer? Thanks.

A:

Hint: $$\dfrac{5}{13}=\dfrac{1}{a+\dfrac{c}{bc+2}}=\dfrac{bc+2}{a(bc+2)+c}\\
\implies a=\dfrac{13(bc+2)-5c}{5(bc+2)}=\dfrac{13}{5}-\dfrac{c}{bc+2}$$

