Algebra Examples

$s = 2 π r^{2} + 2 π r h$

Step 1

Rewrite the equation as $2 π r^{2} + 2 π r h = s$ .

$2 π r^{2} + 2 π r h = s$

Step 2

Subtract $2 π r^{2}$ from both sides of the equation.

$2 π r h = s - 2 π r^{2}$

Step 3

Divide each term in $2 π r h = s - 2 π r^{2}$ by $2 π r$ and simplify.

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Step 3.1

Divide each term in $2 π r h = s - 2 π r^{2}$ by $2 π r$ .

$\frac{2 π r h}{2 π r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 π r h}{2 π r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2.1.2

Rewrite the expression.

$\frac{π r h}{π r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2.2

Cancel the common factor of $π$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{π r h}{π r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2.2.2

Rewrite the expression.

$\frac{r h}{r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2.3

Cancel the common factor of $r$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{r h}{r} = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Step 3.2.3.2

Divide $h$ by $1$ .

$h = \frac{s}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

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 $- 2$ and $2$ .

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Step 3.3.1.1.1

Factor $2$ out of $- 2 π r^{2}$ .

$h = \frac{s}{2 π r} + \frac{2 (- π r^{2})}{2 π r}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $2 π r$ .

$h = \frac{s}{2 π r} + \frac{2 (- π r^{2})}{2 (π r)}$

Step 3.3.1.1.2.2

Cancel the common factor.

$h = \frac{s}{2 π r} + \frac{2 (- π r^{2})}{2 (π r)}$

Step 3.3.1.1.2.3

Rewrite the expression.

$h = \frac{s}{2 π r} + \frac{- π r^{2}}{π r}$

Step 3.3.1.2

Cancel the common factor of $π$ .

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Step 3.3.1.2.1

Cancel the common factor.

$h = \frac{s}{2 π r} + \frac{- π r^{2}}{π r}$

Step 3.3.1.2.2

Rewrite the expression.

$h = \frac{s}{2 π r} + \frac{- 1 r^{2}}{r}$

Step 3.3.1.3

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

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Step 3.3.1.3.1

Factor $r$ out of $- 1 r^{2}$ .

$h = \frac{s}{2 π r} + \frac{r (- 1 r)}{r}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

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

$h = \frac{s}{2 π r} + \frac{r (- 1 r)}{r^{1}}$

Step 3.3.1.3.2.2

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

$h = \frac{s}{2 π r} + \frac{r (- 1 r)}{r \cdot 1}$

Step 3.3.1.3.2.3

Cancel the common factor.

$h = \frac{s}{2 π r} + \frac{r (- 1 r)}{r \cdot 1}$

Step 3.3.1.3.2.4

Rewrite the expression.

$h = \frac{s}{2 π r} + \frac{- 1 r}{1}$

Step 3.3.1.3.2.5

Divide $- 1 r$ by $1$ .

$h = \frac{s}{2 π r} - 1 r$

Step 3.3.1.4

Rewrite $- 1 r$ as $- r$ .

$h = \frac{s}{2 π r} - r$