Finite Math Examples

$\frac{\frac{3 s - s^{2}}{2 t}}{\frac{4 (s^{2} - 9)}{3 t}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 s - s^{2}}{2 t} \cdot \frac{3 t}{4 (s^{2} - 9)}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $t$ .

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Step 2.1.1

Factor $t$ out of $2 t$ .

$\frac{3 s - s^{2}}{t \cdot 2} \cdot \frac{3 t}{4 (s^{2} - 9)}$

Step 2.1.2

Factor $t$ out of $3 t$ .

$\frac{3 s - s^{2}}{t \cdot 2} \cdot \frac{t \cdot 3}{4 (s^{2} - 9)}$

Step 2.1.3

Cancel the common factor.

$\frac{3 s - s^{2}}{t \cdot 2} \cdot \frac{t \cdot 3}{4 (s^{2} - 9)}$

Step 2.1.4

Rewrite the expression.

$\frac{3 s - s^{2}}{2} \cdot \frac{3}{4 (s^{2} - 9)}$

Step 2.2

Multiply $\frac{3 s - s^{2}}{2}$ by $\frac{3}{4 (s^{2} - 9)}$ .

$\frac{(3 s - s^{2}) \cdot 3}{2 (4 (s^{2} - 9))}$

Step 2.3

Multiply $4$ by $2$ .

$\frac{(3 s - s^{2}) \cdot 3}{8 (s^{2} - 9)}$

Step 2.4

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

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Step 2.4.1

Factor $s$ out of $3 s$ .

$\frac{(s \cdot 3 - s^{2}) \cdot 3}{8 (s^{2} - 9)}$

Step 2.4.2

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

$\frac{(s \cdot 3 + s (- s)) \cdot 3}{8 (s^{2} - 9)}$

Step 2.4.3

Factor $s$ out of $s \cdot 3 + s (- s)$ .

$\frac{s (3 - s) \cdot 3}{8 (s^{2} - 9)}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

$\frac{s (3 - s) \cdot 3}{8 (s^{2} - 3^{2})}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = s$ and $b = 3$ .

$\frac{s (3 - s) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $3 - s$ and $s - 3$ .

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Step 4.1.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{s (- 1 (- 3) - s) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4.1.2

Factor $- 1$ out of $- s$ .

$\frac{s (- 1 (- 3) - (s)) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4.1.3

Factor $- 1$ out of $- 1 (- 3) - (s)$ .

$\frac{s (- 1 (- 3 + s)) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4.1.4

Reorder terms.

$\frac{s (- 1 (s - 3)) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4.1.5

Cancel the common factor.

$\frac{s (- 1 (s - 3)) \cdot 3}{8 (s + 3) (s - 3)}$

Step 4.1.6

Rewrite the expression.

$\frac{s \cdot (- 1) \cdot 3}{8 (s + 3)}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Multiply $3$ by $- 1$ .

$\frac{s \cdot - 3}{8 (s + 3)}$

Step 4.2.2

Move $- 3$ to the left of $s$ .

$\frac{- 3 \cdot s}{8 (s + 3)}$

Step 4.2.3

Move the negative in front of the fraction.

$- \frac{3 s}{8 (s + 3)}$