Simplify ((x^2y)/(z^2))/((xy^2)/(z^2))

$\frac{\frac{x^{2} y}{z^{2}}}{\frac{x y^{2}}{z^{2}}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} y}{z^{2}} \cdot \frac{z^{2}}{x y^{2}}$

Combine.

$\frac{x^{2} y z^{2}}{z^{2} (x y^{2})}$

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2} y z^{2}$ .

$\frac{x (x y z^{2})}{z^{2} (x y^{2})}$

Cancel the common factors.

Factor $x$ out of $z^{2} (x y^{2})$ .

$\frac{x (x y z^{2})}{x (z^{2} (y^{2}))}$

Cancel the common factor.

$\frac{x (x y z^{2})}{x (z^{2} (y^{2}))}$

Rewrite the expression.

$\frac{x y z^{2}}{z^{2} (y^{2})}$

Cancel the common factor of $y$ and $y^{2}$ .

Factor $y$ out of $x y z^{2}$ .

$\frac{y (x z^{2})}{z^{2} (y^{2})}$

Cancel the common factors.

Factor $y$ out of $z^{2} (y^{2})$ .

$\frac{y (x z^{2})}{y (z^{2} (y))}$

Cancel the common factor.

$\frac{y (x z^{2})}{y (z^{2} (y))}$

Rewrite the expression.

$\frac{x z^{2}}{z^{2} (y)}$

Cancel the common factor of $z^{2}$ .

Cancel the common factor.

$\frac{x z^{2}}{z^{2} y}$

Rewrite the expression.

$\frac{x}{y}$