Basic Math Examples

$\frac{a f}{b} = f + c - d$

Step 1

Multiply both sides by $b$ .

$\frac{a f}{b} b = (f + c - d) b$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $b$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{a f}{b} b = (f + c - d) b$

Step 2.1.1.2

Rewrite the expression.

$a f = (f + c - d) b$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(f + c - d) b$ .

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Step 2.2.1.1

Apply the distributive property.

$a f = f b + c b - d b$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Reorder $f$ and $b$ .

$a f = b f + c b - d b$

Step 2.2.1.2.2

Reorder $c$ and $b$ .

$a f = b f + b c - d b$

Step 2.2.1.2.3

Move $d$ .

$a f = b f + b c - 1 b d$

Step 2.2.1.2.4

Move $b f$ .

$a f = b c - 1 b d + b f$

Step 3

Solve for $f$ .

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Step 3.1

Rewrite $- 1 b$ as $- b$ .

$a f = b c - b d + b f$

Step 3.2

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

$a f - b f = b c - b d$

Step 3.3

Factor $f$ out of $a f - b f$ .

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Step 3.3.1

Factor $f$ out of $a f$ .

$f a - b f = b c - b d$

Step 3.3.2

Factor $f$ out of $- b f$ .

$f a + f (- b) = b c - b d$

Step 3.3.3

Factor $f$ out of $f a + f (- b)$ .

$f (a - b) = b c - b d$

Step 3.4

Divide each term in $f (a - b) = b c - b d$ by $a - b$ and simplify.

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Step 3.4.1

Divide each term in $f (a - b) = b c - b d$ by $a - b$ .

$\frac{f (a - b)}{a - b} = \frac{b c}{a - b} + \frac{- b d}{a - b}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $a - b$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{f (a - b)}{a - b} = \frac{b c}{a - b} + \frac{- b d}{a - b}$

Step 3.4.2.1.2

Divide $f$ by $1$ .

$f = \frac{b c}{a - b} + \frac{- b d}{a - b}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Combine the numerators over the common denominator.

$f = \frac{b c - b d}{a - b}$

Step 3.4.3.2

Simplify the numerator.

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Step 3.4.3.2.1

Factor $b$ out of $b c - b d$ .

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Step 3.4.3.2.1.1

Factor $b$ out of $b c$ .

$f = \frac{b (c) - b d}{a - b}$

Step 3.4.3.2.1.2

Factor $b$ out of $- b d$ .

$f = \frac{b (c) + b (- 1 d)}{a - b}$

Step 3.4.3.2.1.3

Factor $b$ out of $b (c) + b (- 1 d)$ .

$f = \frac{b (c - 1 d)}{a - b}$

Step 3.4.3.2.2

Rewrite $- 1 d$ as $- d$ .

$f = \frac{b (c - d)}{a - b}$