Basic Math Examples

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

Step 1

Rewrite the equation as $\frac{a + b}{a - b} = d$ .

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

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.

$a - b, 1$

Step 2.2

Remove parentheses.

$a - b, 1$

Step 2.3

The LCM of one and any expression is the expression.

$a - b$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a - b$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

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

Step 3.3.2

Rewrite using the commutative property of multiplication.

$a + b = d a - d b$

Step 4

Solve the equation.

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Step 4.1

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

$a + b - d a = - d b$

Step 4.2

Subtract $b$ from both sides of the equation.

$a - d a = - d b - b$

Step 4.3

Factor $a$ out of $a - d a$ .

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Step 4.3.1

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

$a \cdot 1 - d a = - d b - b$

Step 4.3.2

Factor $a$ out of $- d a$ .

$a \cdot 1 + a (- d) = - d b - b$

Step 4.3.3

Factor $a$ out of $a \cdot 1 + a (- d)$ .

$a (1 - d) = - d b - b$

Step 4.4

Divide each term in $a (1 - d) = - d b - b$ by $1 - d$ and simplify.

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Step 4.4.1

Divide each term in $a (1 - d) = - d b - b$ by $1 - d$ .

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $1 - d$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $a$ by $1$ .

$a = \frac{- d b}{1 - d} + \frac{- b}{1 - d}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$a = \frac{- d b - b}{1 - d}$

Step 4.4.3.2

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

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Step 4.4.3.2.1

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

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

Step 4.4.3.2.2

Factor $b$ out of $- b$ .

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

Step 4.4.3.2.3

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

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

Step 4.4.3.3

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

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

Step 4.4.3.4

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

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

Step 4.4.3.5

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

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

Step 4.4.3.6

Simplify the expression.

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Step 4.4.3.6.1

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

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

Step 4.4.3.6.2

Move the negative in front of the fraction.

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