Basic Math Examples

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

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

Step 1

Rewrite the equation as

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

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

\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

$a - b, 1$

Step 2.2

Remove parentheses.

a - b, 1

$a - b, 1$

Step 2.3

The LCM of one and any expression is the expression.

a - b

$a - b$

a - b

$a - b$

Step 3

Multiply each term in

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

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

a - b

$a - b$ to eliminate the fractions.

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Step 3.1

Multiply each term in

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

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

a - b

$a - b$ .

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

$a - b$ .

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Step 3.2.1.1

Cancel the common factor.

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

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

Step 3.2.1.2

Rewrite the expression.

a + b = d (a - b)

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

a + b = d (a - b)

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

a + b = d (a - b)

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

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)

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

Step 3.3.2

Rewrite using the commutative property of multiplication.

a + b = d a - d b

$a + b = d a - d b$

a + b = d a - d b

$a + b = d a - d b$

a + b = d a - d b

$a + b = d a - d b$

Step 4

Solve the equation.

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Step 4.1

Subtract

d a

$d a$ from both sides of the equation.

a + b - d a = - d b

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

Step 4.2

Subtract

b

$b$ from both sides of the equation.

a - d a = - d b - b

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

Step 4.3

Factor

a

$a$ out of

a - d a

$a - d a$ .

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Step 4.3.1

Factor

a

$a$ out of

a^{1}

$a^{1}$ .

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

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

Step 4.3.2

Factor

a

$a$ out of

- d a

$- d a$ .

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

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

Step 4.3.3

Factor

a

$a$ out of

a \cdot 1 + a (- d)

$a \cdot 1 + a (- d)$ .

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

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

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

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

Step 4.4

Divide each term in

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

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

1 - d

$1 - d$ and simplify.

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Step 4.4.1

Divide each term in

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

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

1 - d

$1 - d$ .

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

$1 - d$ .

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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}

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

Step 4.4.2.1.2

Divide

a

$a$ by

1

$1$ .

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

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

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

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

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

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

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}

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

Step 4.4.3.2

Factor

b

$b$ out of

- d b - b

$- d b - b$ .

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Step 4.4.3.2.1

Factor

b

$b$ out of

- d b

$- d b$ .

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

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

Step 4.4.3.2.2

Factor

b

$b$ out of

- b

$- b$ .

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

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

Step 4.4.3.2.3

Factor

b

$b$ out of

b (- d) + b \cdot - 1

$b (- d) + b \cdot - 1$ .

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

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

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

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

Step 4.4.3.3

Factor

- 1

$- 1$ out of

- d

$- d$ .

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

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

Step 4.4.3.4

Rewrite

- 1

$- 1$ as

- 1 (1)

$- 1 (1)$ .

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

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

Step 4.4.3.5

Factor

- 1

$- 1$ out of

- (d) - 1 (1)

$- (d) - 1 (1)$ .

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

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

Step 4.4.3.6

Simplify the expression.

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Step 4.4.3.6.1

Rewrite

- (d + 1)

$- (d + 1)$ as

- 1 (d + 1)

$- 1 (d + 1)$ .

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

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

Step 4.4.3.6.2

Move the negative in front of the fraction.

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