Algebra Examples

$f = \frac{f g}{f + g - d}$

Step 1

Rewrite the equation as $\frac{f g}{f + g - d} = f$ .

$\frac{f g}{f + g - d} = f$

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.

$f + g - d, 1$

Step 2.2

Remove parentheses.

$f + g - d, 1$

Step 2.3

The LCM of one and any expression is the expression.

$f + g - d$

Step 3

Multiply each term in $\frac{f g}{f + g - d} = f$ by $f + g - d$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{f g}{f + g - d} = f$ by $f + g - d$ .

$\frac{f g}{f + g - d} (f + g - d) = f (f + g - d)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $f + g - d$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{f g}{f + g - d} (f + g - d) = f (f + g - d)$

Step 3.2.1.2

Rewrite the expression.

$f g = f (f + g - d)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$f g = f \cdot f + f g + f (- d)$

Step 3.3.2

Simplify.

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Step 3.3.2.1

Multiply $f$ by $f$ .

$f g = f^{2} + f g + f (- d)$

Step 3.3.2.2

Rewrite using the commutative property of multiplication.

$f g = f^{2} + f g - f d$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $f^{2} + f g - f d = f g$ .

$f^{2} + f g - f d = f g$

Step 4.2

Move all terms not containing $d$ to the right side of the equation.

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Step 4.2.1

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

$f g - f d = f g - f^{2}$

Step 4.2.2

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

$- f d = f g - f^{2} - f g$

Step 4.2.3

Combine the opposite terms in $f g - f^{2} - f g$ .

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Step 4.2.3.1

Subtract $f g$ from $f g$ .

$- f d = - f^{2} + 0$

Step 4.2.3.2

Add $- f^{2}$ and $0$ .

$- f d = - f^{2}$

Step 4.3

Divide each term in $- f d = - f^{2}$ by $- f$ and simplify.

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Step 4.3.1

Divide each term in $- f d = - f^{2}$ by $- f$ .

$\frac{- f d}{- f} = \frac{- f^{2}}{- f}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{f d}{f} = \frac{- f^{2}}{- f}$

Step 4.3.2.2

Cancel the common factor of $f$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{f d}{f} = \frac{- f^{2}}{- f}$

Step 4.3.2.2.2

Divide $d$ by $1$ .

$d = \frac{- f^{2}}{- f}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

$d = \frac{f^{2}}{f}$

Step 4.3.3.2

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

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Step 4.3.3.2.1

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

$d = \frac{f \cdot f}{f}$

Step 4.3.3.2.2

Cancel the common factors.

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Step 4.3.3.2.2.1

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

$d = \frac{f \cdot f}{f^{1}}$

Step 4.3.3.2.2.2

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

$d = \frac{f \cdot f}{f \cdot 1}$

Step 4.3.3.2.2.3

Cancel the common factor.

$d = \frac{f \cdot f}{f \cdot 1}$

Step 4.3.3.2.2.4

Rewrite the expression.

$d = \frac{f}{1}$

Step 4.3.3.2.2.5

Divide $f$ by $1$ .

$d = f$