Algebra Examples

$\frac{6 x^{2} y}{z} \div \frac{3 x y^{2}}{z}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 x^{2} y}{z} \cdot \frac{z}{3 x y^{2}}$

Step 2

Combine.

$\frac{6 x^{2} y z}{z (3 x y^{2})}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

Factor $3$ out of $6 x^{2} y z$ .

$\frac{3 (2 x^{2} y z)}{z (3 x y^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $z (3 x y^{2})$ .

$\frac{3 (2 x^{2} y z)}{3 (z (x y^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (2 x^{2} y z)}{3 (z (x y^{2}))}$

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

Factor $y$ out of $2 x y z$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

Cancel the common factor of $z$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{2 x}{y}$

$\frac{2 x}{y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$