Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{x}{y}$