Simplify 3x-(y·z+3z:z/x): Multiple Variable Expression Solution

To solve this problem, we begin by simplifying the expression inside the parentheses: $y \cdot z + 3z : \frac{z}{x}$.

First, evaluate the division: $\frac{3z}{\frac{z}{x}}$. This can be simplified by multiplying by the reciprocal, yielding $3z \cdot \frac{x}{z} = 3x$.

The expression inside the parentheses becomes $y \cdot z + 3x$.

Now substitute this back into the entire expression: $3x - (y \cdot z + 3x)$.

Apply the distributive property to the negative sign, resulting in: $3x - y \cdot z - 3x$.

Combine like terms: $3x - 3x - y \cdot z$ simplifies to $- y \cdot z$.

Thus, the solution to the given expression is $-yz$.