Find the domain of the Equation: (√15 + 34/z)/(4y-12+4) = 5

To determine the field of application (domain of definition) of the given equation, we need to identify all values of the variables that would make the equation undefined.

The given equation is:
$\frac{\sqrt{15}+34:z}{4y-12+8:2}=5$

where the colon (:) represents division, so we can rewrite this as:
$\frac{\sqrt{15}+\frac{34}{z}}{4y-12+\frac{8}{2}}=5$

Step 1: Identify potential division by zero in the numerator
In the numerator, we have the term $\frac{34}{z}$. This expression is undefined when $z = 0$.
Therefore, we must have: $z \neq 0$

Step 2: Simplify and analyze the denominator
The denominator is: $4y-12+\frac{8}{2}$
Simplifying: $4y-12+4 = 4y-8$

Step 3: Identify when the denominator equals zero
The entire fraction is undefined when the denominator equals zero:
$4y-8 = 0$
$4y = 8$
$y = 2$

Therefore, we must have: $y \neq 2$

Step 4: State the domain (field of application)
The equation is defined for all values of $y$ and $z$ except those that cause division by zero.

Therefore, the field of application of the equation is: $z \neq 0$ and $y \neq 2$

This corresponds to choice 3.