Algebra Examples

$\frac{6 x^{5} y^{2} - 3 x^{2} y^{3}}{3 x^{4} y}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3 x^{2} y^{2}$ out of $6 x^{5} y^{2} - 3 x^{2} y^{3}$ .

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Step 1.1.1

Factor $3 x^{2} y^{2}$ out of $6 x^{5} y^{2}$ .

$\frac{3 x^{2} y^{2} (2 x^{3}) - 3 x^{2} y^{3}}{3 x^{4} y}$

Step 1.1.2

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

$\frac{3 x^{2} y^{2} (2 x^{3}) + 3 x^{2} y^{2} (- 1 y)}{3 x^{4} y}$

Step 1.1.3

Factor $3 x^{2} y^{2}$ out of $3 x^{2} y^{2} (2 x^{3}) + 3 x^{2} y^{2} (- 1 y)$ .

$\frac{3 x^{2} y^{2} (2 x^{3} - 1 y)}{3 x^{4} y}$

Step 1.2

Rewrite $- 1 y$ as $- y$ .

$\frac{3 x^{2} y^{2} (2 x^{3} - y)}{3 x^{4} y}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 x^{2} y^{2} (2 x^{3} - y)}{3 x^{4} y}$

Step 2.1.2

Rewrite the expression.

$\frac{x^{2} y^{2} (2 x^{3} - y)}{x^{4} y}$

Step 2.2

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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Step 2.2.1

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

$\frac{x^{2} (y^{2} (2 x^{3} - y))}{x^{4} y}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{2}$ out of $x^{4} y$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

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

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

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