Calculus Examples

$f (t) = \frac{3}{t^{2} - t}$

Step 1

Set the denominator in $\frac{3}{t^{2} - t}$ equal to $0$ to find where the expression is undefined.

$t^{2} - t = 0$

Step 2

Solve for $t$ .

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Step 2.1

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

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Step 2.1.1

Factor $t$ out of $t^{2}$ .

$t \cdot t - t = 0$

Step 2.1.2

Factor $t$ out of $- t$ .

$t \cdot t + t \cdot - 1 = 0$

Step 2.1.3

Factor $t$ out of $t \cdot t + t \cdot - 1$ .

$t (t - 1) = 0$

Step 2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$t = 0$

$t - 1 = 0$

Step 2.3

Set $t$ equal to $0$ .

$t = 0$

Step 2.4

Set $t - 1$ equal to $0$ and solve for $t$ .

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Step 2.4.1

Set $t - 1$ equal to $0$ .

$t - 1 = 0$

Step 2.4.2

Add $1$ to both sides of the equation.

$t = 1$

Step 2.5

The final solution is all the values that make $t (t - 1) = 0$ true.

$t = 0, 1$

Step 3

The domain is all values of $t$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, 1) \cup (1, \infty)$

Set-Builder Notation:

${t | t \neq 0, 1}$

Step 4