Basic Math Examples

$\frac{s^{3} - s^{2} y}{s y} \cdot \frac{3 y}{3 s - 3 y}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Factor $s^{2}$ out of $s^{3}$ .

$\frac{s^{2} s - s^{2} y}{s y} \cdot \frac{3 y}{3 s - 3 y}$

Step 1.1.2

Factor $s^{2}$ out of $- s^{2} y$ .

$\frac{s^{2} s + s^{2} (- 1 y)}{s y} \cdot \frac{3 y}{3 s - 3 y}$

Step 1.1.3

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

$\frac{s^{2} (s - 1 y)}{s y} \cdot \frac{3 y}{3 s - 3 y}$

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 s - 3 y$ .

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Step 2.1.1

Factor $3$ out of $3 s$ .

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

Step 2.1.2

Factor $3$ out of $- 3 y$ .

$\frac{s^{2} (s - y)}{s y} \cdot \frac{3 y}{3 (s) + 3 (- y)}$

Step 2.1.3

Factor $3$ out of $3 (s) + 3 (- y)$ .

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

Step 2.2

Combine.

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

Step 2.3

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

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Step 2.3.1

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

$\frac{s ((s (s - y)) (3 y))}{s y (3 (s - y))}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $s$ out of $s y (3 (s - y))$ .

$\frac{s ((s (s - y)) (3 y))}{s (y (3 (s - y)))}$

Step 2.3.2.2

Cancel the common factor.

$\frac{s ((s (s - y)) (3 y))}{s (y (3 (s - y)))}$

Step 2.3.2.3

Rewrite the expression.

$\frac{(s (s - y)) (3 y)}{y (3 (s - y))}$

Step 2.4

Cancel the common factor of $s - y$ .

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Step 2.4.1

Cancel the common factor.

$\frac{s (s - y) (3 y)}{y (3 (s - y))}$

Step 2.4.2

Rewrite the expression.

$\frac{(s) (3 y)}{y \cdot (3)}$

Step 2.5

Cancel the common factor of $3$ .

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Step 2.5.1

Cancel the common factor.

$\frac{s (3 y)}{y \cdot 3}$

Step 2.5.2

Rewrite the expression.

$\frac{(s) (y)}{y}$

Step 2.6

Cancel the common factor of $y$ .

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Step 2.6.1

Cancel the common factor.

$\frac{s y}{y}$

Step 2.6.2

Divide $s$ by $1$ .

$s$