Question

find the sum of x+y+z

Answer 1

Since x, y and z are natural numbers, x, y and z are >= 1 and are integers. So separate fraction and integer parts...

$\frac{35}{13}-2=\frac{1}{x+\frac{1}{y+\frac{1}{z}}}\\\\\\\frac{13}{9}=x+\frac{1}{y+\frac{1}{z}}\\\\So \: x=1 \: and \: \frac{4}{9}=\frac{1}{y+\frac{1}{z}}\\\\Reciprocate \: both \: sides\\So \: y = 2. \: and \: \frac{1}{4}=\frac{1}{z}\\\\x=1, \: y=2. \: z=4.\\\\x+y+z=7.$