Precalculus Examples

$h (t) = 12 t^{2} - 6 t + 50$

Step 1

Divide each term in $h t = 12 t^{2} - 6 t + 50$ by $t$ .

$\frac{h t}{t} = \frac{12 t^{2}}{t} + \frac{- 6 t}{t} + \frac{50}{t}$

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.

$\frac{h t}{t} = \frac{12 t^{2}}{t} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 2.1.2

Divide $h$ by $1$ .

$h = \frac{12 t^{2}}{t} + \frac{- 6 t}{t} + \frac{50}{t}$

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 $t^{2}$ and $t$ .

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Step 3.1.1.1

Factor $t$ out of $12 t^{2}$ .

$h = \frac{t (12 t)}{t} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.1.2

Cancel the common factors.

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Step 3.1.1.2.1

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

$h = \frac{t (12 t)}{t^{1}} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.1.2.2

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

$h = \frac{t (12 t)}{t \cdot 1} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.1.2.3

Cancel the common factor.

$h = \frac{t (12 t)}{t \cdot 1} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.1.2.4

Rewrite the expression.

$h = \frac{12 t}{1} + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.1.2.5

Divide $12 t$ by $1$ .

$h = 12 t + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.2

Cancel the common factor of $t$ .

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Step 3.1.2.1

Cancel the common factor.

$h = 12 t + \frac{- 6 t}{t} + \frac{50}{t}$

Step 3.1.2.2

Divide $- 6$ by $1$ .

$h = 12 t - 6 + \frac{50}{t}$