Fraction equation involving variables x and y with missing digits represented by boxes.

- The equation shown is $\frac{\square \cdot x \cdot y}{\square \cdot y} = \frac{\square \cdot x \cdot y}{\square \cdot x}$.
- To solve this, we need to find values for the squares (□) that make the equation true for all valid $x$ and $y$ (assuming $x \neq 0$, $y \neq 0$ to avoid division by zero).
- Simplify both sides of the equation by canceling common factors.
- On the left side: $\frac{\square \cdot x \cdot y}{\square \cdot y}$. The $y$ in the numerator and denominator cancels out, leaving $\frac{\square \cdot x}{\square}$.
- On the right side: $\frac{\square \cdot x \cdot y}{\square \cdot x}$. The $x$ in the numerator and denominator cancels out, leaving $\frac{\square \cdot y}{\square}$.
- So the simplified equation is: $\frac{\square \cdot x}{\square} = \frac{\square \cdot y}{\square}$.
- For this to be true for all $x$ and $y$, the only way is if the coefficient (the value in the square) on the left is zero, or the coefficient on the right is zero, or both coefficients are zero. But if any coefficient is zero, the entire fraction becomes zero (as long as the denominator is not zero), so we get $0 = 0$, which is true.
- However, if we assume the squares represent non-zero constants, then for $\frac{a \cdot x}{b} = \frac{c \cdot y}{d}$ to hold for all $x$ and $y$, it must be that $a/b = 0$ and $c/d = 0$, which implies $a=0$ and $c=0$.
- Alternatively, if we interpret the squares as placeholders for the same value (i.e., all squares are equal), let’s denote the value as $k$.
- Then the equation becomes: $\frac{k \cdot x \cdot y}{k \cdot y} = \frac{k \cdot x \cdot y}{k \cdot x}$.
- Simplifying both sides: Left side becomes $\frac{kxy}{ky} = x$ (if $k \neq 0$, $y \neq 0$). Right side becomes $\frac{kxy}{kx} = y$ (if $k \neq 0$, $x \neq 0$).
- So we have $x = y$.
- But the problem likely expects an identity (true for all $x$ and $y$), not a conditional equality.
- Therefore, the only consistent solution across all interpretations is that the squares must be zero, making both sides zero.
- Final answer: All squares should be filled with 0.