Precalculus Examples

$T = g r + g v t$

Step 1

Rewrite the equation as $g r + g v t = T$ .

$g r + g v t = T$

Step 2

Subtract $g r$ from both sides of the equation.

$g v t = T - g r$

Step 3

Divide each term in $g v t = T - g r$ by $g v$ and simplify.

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Step 3.1

Divide each term in $g v t = T - g r$ by $g v$ .

$\frac{g v t}{g v} = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $g$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{g v t}{g v} = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.2.1.2

Rewrite the expression.

$\frac{v t}{v} = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.2.2

Cancel the common factor of $v$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{v t}{v} = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.2.2.2

Divide $t$ by $1$ .

$t = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $g$ .

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Step 3.3.1.1.1

Cancel the common factor.

$t = \frac{T}{g v} + \frac{- g r}{g v}$

Step 3.3.1.1.2

Rewrite the expression.

$t = \frac{T}{g v} + \frac{- 1 r}{v}$

Step 3.3.1.2

Move the negative in front of the fraction.

$t = \frac{T}{g v} - \frac{r}{v}$