Precalculus Examples

f = \frac{m v^{2}}{r}

$f = \frac{m v^{2}}{r}$

Step 1

Rewrite the equation as

\frac{m v^{2}}{r} = f

$\frac{m v^{2}}{r} = f$ .

\frac{m v^{2}}{r} = f

$\frac{m v^{2}}{r} = f$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

r, 1

$r, 1$

Step 2.2

The LCM of one and any expression is the expression.

r

$r$

r

$r$

Step 3

Multiply each term in

\frac{m v^{2}}{r} = f

$\frac{m v^{2}}{r} = f$ by

r

$r$ to eliminate the fractions.

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Step 3.1

Multiply each term in

\frac{m v^{2}}{r} = f

$\frac{m v^{2}}{r} = f$ by

r

$r$ .

\frac{m v^{2}}{r} r = f r

$\frac{m v^{2}}{r} r = f r$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

r

$r$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{m v^{2}}{r} r = f r$

Step 3.2.1.2

Rewrite the expression.

$m v^{2} = f r$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as

$f r = m v^{2}$ .

$f r = m v^{2}$

Step 4.2

Divide each term in

$f r = m v^{2}$ by

$f$ and simplify.

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Step 4.2.1

Divide each term in

$f r = m v^{2}$ by

$f$ .

$\frac{f r}{f} = \frac{m v^{2}}{f}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

$f$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{f r}{f} = \frac{m v^{2}}{f}$

Step 4.2.2.1.2

Divide

$r$ by

$1$ .

$r = \frac{m v^{2}}{f}$

$f = \frac{m v^{2}}{r}$

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