Basic Math Examples

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

Step 1

Move all terms containing variables to the left side of the equation.

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Step 1.1

Subtract $\frac{b f}{b}$ from both sides of the equation.

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

Step 1.2

Subtract $c$ from both sides of the equation.

$\frac{a f}{b} + d - \frac{b f}{b} - c = 0$

Step 1.3

Cancel the common factor of $b$ .

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Step 1.3.1

Cancel the common factor.

$\frac{a f}{b} + d - \frac{b f}{b} - c = 0$

Step 1.3.2

Divide $f$ by $1$ .

$\frac{a f}{b} + d - f - c = 0$

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.

$b, 1, 1, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$b$

Step 3

Multiply each term in $\frac{a f}{b} + d - f - c = 0$ by $b$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a f}{b} + d - f - c = 0$ by $b$ .

$\frac{a f}{b} b + d b - f b - c b = 0 b$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $b$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a f}{b} b + d b - f b - c b = 0 b$

Step 3.2.1.2

Rewrite the expression.

$a f + d b - f b - c b = 0 b$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $0$ by $b$ .

$a f + d b - f b - c b = 0$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Add $c b$ to both sides of the equation.

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

Step 4.2

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

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Step 4.2.1

Factor $f$ out of $a f$ .

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

Step 4.2.2

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

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

Step 4.2.3

Factor $f$ out of $f a + f (- 1 b)$ .

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

Step 4.3

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

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

Step 4.4

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

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Step 4.4.1

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

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $a - b$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $f$ by $1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

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

Step 4.4.3.2

Combine the numerators over the common denominator.

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

Step 4.4.3.3

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

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Step 4.4.3.3.1

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

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

Step 4.4.3.3.2

Factor $b$ out of $c b$ .

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

Step 4.4.3.3.3

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

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

Step 4.4.3.4

Factor $- 1$ out of $- d$ .

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

Step 4.4.3.5

Factor $- 1$ out of $c$ .

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

Step 4.4.3.6

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

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

Step 4.4.3.7

Simplify the expression.

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Step 4.4.3.7.1

Rewrite $- (d - c)$ as $- 1 (d - c)$ .

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

Step 4.4.3.7.2

Move the negative in front of the fraction.

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