Finite Math Examples

$f (t) = \frac{t}{t^{2} - 9}$

Step 1

Set $\frac{t}{t^{2} - 9}$ equal to $0$ .

$\frac{t}{t^{2} - 9} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor each term.

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Step 2.1.1

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

$\frac{t}{t^{2} - 3^{2}} = 0$

Step 2.1.2

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

$\frac{t}{(t + 3) (t - 3)} = 0$

Step 2.2

Find the LCD of the terms in the equation.

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Step 2.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$(t + 3) (t - 3), 1$

Step 2.2.2

The LCM of one and any expression is the expression.

$(t + 3) (t - 3)$

Step 2.3

Multiply each term in $\frac{t}{(t + 3) (t - 3)} = 0$ by $(t + 3) (t - 3)$ to eliminate the fractions.

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Step 2.3.1

Multiply each term in $\frac{t}{(t + 3) (t - 3)} = 0$ by $(t + 3) (t - 3)$ .

$\frac{t}{(t + 3) (t - 3)} ((t + 3) (t - 3)) = 0 ((t + 3) (t - 3))$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $(t + 3) (t - 3)$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{t}{(t + 3) (t - 3)} ((t + 3) (t - 3)) = 0 ((t + 3) (t - 3))$

Step 2.3.2.1.2

Rewrite the expression.

$t = 0 ((t + 3) (t - 3))$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Expand $(t + 3) (t - 3)$ using the FOIL Method.

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Step 2.3.3.1.1

Apply the distributive property.

$t = 0 (t (t - 3) + 3 (t - 3))$

Step 2.3.3.1.2

Apply the distributive property.

$t = 0 (t \cdot t + t \cdot - 3 + 3 (t - 3))$

Step 2.3.3.1.3

Apply the distributive property.

$t = 0 (t \cdot t + t \cdot - 3 + 3 t + 3 \cdot - 3)$

Step 2.3.3.2

Simplify terms.

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Step 2.3.3.2.1

Combine the opposite terms in $t \cdot t + t \cdot - 3 + 3 t + 3 \cdot - 3$ .

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Step 2.3.3.2.1.1

Reorder the factors in the terms $t \cdot - 3$ and $3 t$ .

$t = 0 (t \cdot t - 3 t + 3 t + 3 \cdot - 3)$

Step 2.3.3.2.1.2

Add $- 3 t$ and $3 t$ .

$t = 0 (t \cdot t + 0 + 3 \cdot - 3)$

Step 2.3.3.2.1.3

Add $t \cdot t$ and $0$ .

$t = 0 (t \cdot t + 3 \cdot - 3)$

Step 2.3.3.2.2

Simplify each term.

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Step 2.3.3.2.2.1

Multiply $t$ by $t$ .

$t = 0 (t^{2} + 3 \cdot - 3)$

Step 2.3.3.2.2.2

Multiply $3$ by $- 3$ .

$t = 0 (t^{2} - 9)$

Step 2.3.3.2.3

Multiply $0$ by $t^{2} - 9$ .

$t = 0$

Step 3