Solve for a d=(a+b)/(a-b)

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

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

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

Solve for $a$ .

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Multiply each term by $a - b$ and simplify.

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

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

Cancel the common factor of $a - b$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify $d \cdot (a - b)$ .

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Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

$a + b = d a - d b$

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

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

Subtract $b$ from both sides of the equation.

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

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

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

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

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

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

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

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

Divide each term by $1 - d$ and simplify.

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

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

Cancel the common factor of $1 - d$ .

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Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify $\frac{- d b}{1 - d} + \frac{- b}{1 - d}$ .

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Simplify each term.

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Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

Simplify terms.

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Combine the numerators over the common denominator.

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

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

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

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

Factor $b$ out of $- b$ .

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

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

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

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

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

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

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

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

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

Solve for a d=(a+b)/(a-b)

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