Algebra Examples

$M = \frac{L}{F} (\frac{25}{f} + 1)$

Step 1

Rewrite the equation as $\frac{L}{F} \cdot (\frac{25}{f} + 1) = M$ .

$\frac{L}{F} \cdot (\frac{25}{f} + 1) = M$

Step 2

Simplify $\frac{L}{F} \cdot (\frac{25}{f} + 1)$ .

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Step 2.1

Multiply $\frac{L}{F}$ by $\frac{25}{f} + 1$ .

$\frac{L (\frac{25}{f} + 1)}{F} = M$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{L (\frac{25}{f} + \frac{f}{f})}{F} = M$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{L \frac{25 + f}{f}}{F} = M$

Step 2.3

Combine $L$ and $\frac{25 + f}{f}$ .

$\frac{\frac{L (25 + f)}{f}}{F} = M$

Step 2.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{L (25 + f)}{f} \cdot \frac{1}{F} = M$

Step 2.5

Multiply $\frac{L (25 + f)}{f}$ by $\frac{1}{F}$ .

$\frac{L (25 + f)}{f F} = M$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$f F, 1$

Step 3.2

The LCM of one and any expression is the expression.

$f F$

Step 4

Multiply each term in $\frac{L (25 + f)}{f F} = M$ by $f F$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{L (25 + f)}{f F} = M$ by $f F$ .

$\frac{L (25 + f)}{f F} (f F) = M (f F)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $f F$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{L (25 + f)}{f F} (f F) = M (f F)$

Step 4.2.1.2

Rewrite the expression.

$L (25 + f) = M (f F)$

Step 4.2.2

Apply the distributive property.

$L \cdot 25 + L f = M (f F)$

Step 4.2.3

Move $25$ to the left of $L$ .

$25 L + L f = M (f F)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Remove parentheses.

$25 L + L f = M f F$

Step 5

Solve the equation.

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Step 5.1

Subtract $M f F$ from both sides of the equation.

$25 L + L f - M f F = 0$

Step 5.2

Subtract $25 L$ from both sides of the equation.

$L f - M f F = - 25 L$

Step 5.3

Factor $f$ out of $L f - M f F$ .

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Step 5.3.1

Factor $f$ out of $L f$ .

$f L - M f F = - 25 L$

Step 5.3.2

Factor $f$ out of $- M f F$ .

$f L + f (- M F) = - 25 L$

Step 5.3.3

Factor $f$ out of $f L + f (- M F)$ .

$f (L - M F) = - 25 L$

Step 5.4

Divide each term in $f (L - M F) = - 25 L$ by $L - M F$ and simplify.

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Step 5.4.1

Divide each term in $f (L - M F) = - 25 L$ by $L - M F$ .

$\frac{f (L - M F)}{L - M F} = \frac{- 25 L}{L - M F}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $L - M F$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{f (L - M F)}{L - M F} = \frac{- 25 L}{L - M F}$

Step 5.4.2.1.2

Divide $f$ by $1$ .

$f = \frac{- 25 L}{L - M F}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

$f = - \frac{25 L}{L - M F}$