Solve (x·y·z) ÷ (xy/z): Complex Variable Expression Division

Division by a fraction is the same as multiplication by its reciprocal. So $\div \frac{xy}{z}$ becomes $\times \frac{z}{xy}$. This makes the problem much easier to solve!

Look for identical variables in the numerator and denominator. In $\frac{xyz \times z}{xy}$, the x and y appear in both top and bottom, so they cancel completely.

Subtract the exponents when canceling! For example, $\frac{x^3}{x^2} = x^{3-2} = x^1 = x$. In our problem, we have $\frac{z^2}{z^0} = z^2$ since z only appears in the numerator.

Absolutely! Try x=2, y=3, z=4. Original expression: $(2 \times 3 \times 4) \div \frac{2 \times 3}{4} = 24 \div 1.5 = 16$. Our answer $z^2 = 4^2 = 16$ ✓

Be careful! If x or y equals zero, the fraction $\frac{xy}{z}$ becomes zero, and you'd be dividing by zero (undefined). If z equals zero, the original fraction is undefined.