Basic Math Examples

$P = \frac{v (V - v)}{g}$

Step 1

Rewrite the equation as $\frac{v (V - v)}{g} = P$ .

$\frac{v (V - v)}{g} = P$

Step 2

Multiply both sides by $g$ .

$\frac{v (V - v)}{g} g = P g$

Step 3

Simplify the left side.

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Step 3.1

Simplify $\frac{v (V - v)}{g} g$ .

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Step 3.1.1

Cancel the common factor of $g$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{v (V - v)}{g} g = P g$

Step 3.1.1.2

Rewrite the expression.

$v (V - v) = P g$

$v (V - v) = P g$

Step 3.1.2

Apply the distributive property.

$v V + v (- v) = P g$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$v V - v \cdot v = P g$

Step 3.1.4

Multiply $v$ by $v$ by adding the exponents.

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Step 3.1.4.1

Move $v$ .

$v V - (v \cdot v) = P g$

Step 3.1.4.2

Multiply $v$ by $v$ .

$v V - v^{2} = P g$

$v V - v^{2} = P g$

$v V - v^{2} = P g$

$v V - v^{2} = P g$

Step 4

Solve for $V$ .

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Step 4.1

Add $v^{2}$ to both sides of the equation.

$v V = P g + v^{2}$

Step 4.2

Divide each term in $v V = P g + v^{2}$ by $v$ and simplify.

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Step 4.2.1

Divide each term in $v V = P g + v^{2}$ by $v$ .

$\frac{v V}{v} = \frac{P g}{v} + \frac{v^{2}}{v}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $v$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{v V}{v} = \frac{P g}{v} + \frac{v^{2}}{v}$

Step 4.2.2.1.2

Divide $V$ by $1$ .

$V = \frac{P g}{v} + \frac{v^{2}}{v}$

$V = \frac{P g}{v} + \frac{v^{2}}{v}$

$V = \frac{P g}{v} + \frac{v^{2}}{v}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

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

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Step 4.2.3.1.1

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

$V = \frac{P g}{v} + \frac{v \cdot v}{v}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

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

$V = \frac{P g}{v} + \frac{v \cdot v}{v^{1}}$

Step 4.2.3.1.2.2

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

$V = \frac{P g}{v} + \frac{v \cdot v}{v \cdot 1}$

Step 4.2.3.1.2.3

Cancel the common factor.

$V = \frac{P g}{v} + \frac{v \cdot v}{v \cdot 1}$

Step 4.2.3.1.2.4

Rewrite the expression.

$V = \frac{P g}{v} + \frac{v}{1}$

Step 4.2.3.1.2.5

Divide $v$ by $1$ .

$V = \frac{P g}{v} + v$

$V = \frac{P g}{v} + v$

$V = \frac{P g}{v} + v$

$V = \frac{P g}{v} + v$

$V = \frac{P g}{v} + v$

$V = \frac{P g}{v} + v$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$