Precalculus Examples

$H (t) = 18 t - 3 t^{2}$

Step 1

Divide each term in $H t = 18 t - 3 t^{2}$ by $t$ .

$\frac{H t}{t} = \frac{18 t}{t} + \frac{- 3 t^{2}}{t}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $t$ .

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Step 2.1.1

Cancel the common factor.

$\frac{H t}{t} = \frac{18 t}{t} + \frac{- 3 t^{2}}{t}$

Step 2.1.2

Divide $H$ by $1$ .

$H = \frac{18 t}{t} + \frac{- 3 t^{2}}{t}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $t$ .

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Step 3.1.1.1

Cancel the common factor.

$H = \frac{18 t}{t} + \frac{- 3 t^{2}}{t}$

Step 3.1.1.2

Divide $18$ by $1$ .

$H = 18 + \frac{- 3 t^{2}}{t}$

Step 3.1.2

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

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Step 3.1.2.1

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

$H = 18 + \frac{t (- 3 t)}{t}$

Step 3.1.2.2

Cancel the common factors.

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Step 3.1.2.2.1

Raise $t$ to the power of $1$ .

$H = 18 + \frac{t (- 3 t)}{t^{1}}$

Step 3.1.2.2.2

Factor $t$ out of $t^{1}$ .

$H = 18 + \frac{t (- 3 t)}{t \cdot 1}$

Step 3.1.2.2.3

Cancel the common factor.

$H = 18 + \frac{t (- 3 t)}{t \cdot 1}$

Step 3.1.2.2.4

Rewrite the expression.

$H = 18 + \frac{- 3 t}{1}$

Step 3.1.2.2.5

Divide $- 3 t$ by $1$ .

$H = 18 - 3 t$