Solve for x: Finding the Multiplicative Inverse in x·y Expression

Writing $x \div (x \cdot y)$ as $\frac{x}{x \cdot y}$ makes it easier to see what cancels. The fraction form clearly shows the numerator and denominator.

Yes, but be careful! You can only cancel variables that appear as factors (being multiplied), not as terms (being added or subtracted). In $\frac{x}{x \cdot y}$, x is a factor in both parts.

Great question! If $x = 0$, then the original expression $x \div (x \cdot y)$ becomes $0 \div 0$, which is undefined. We assume $x ≠ 0$ for this problem.

Many students think $\frac{x}{x \cdot y} = 1$, but that's incomplete cancellation! When you cancel the x's, you get $\frac{1}{y}$, not 1. The y stays in the denominator.

Multiply your answer by the original divisor: $\frac{1}{y} \times (x \cdot y) = \frac{x \cdot y}{y} = x$. Since you get back to x, your answer is correct!