Solve for a y=x((ab)/(a-b))

$y = x (\frac{a b}{a - b})$

Rewrite the equation as $x (\frac{a b}{a - b}) = y$ .

$x (\frac{a b}{a - b}) = y$

Combine $x$ and $\frac{a b}{a - b}$ .

$\frac{x a b}{a - b} = y$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a - b, 1$

Remove parentheses.

$a - b, 1$

The LCM of one and any expression is the expression.

$a - b$

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

Multiply each term in $\frac{x a b}{a - b} = y$ by $a - b$ .

$\frac{x a b}{a - b} (a - b) = y (a - b)$

Simplify the left side.

Cancel the common factor of $a - b$ .

Cancel the common factor.

$\frac{x a b}{a - b} (a - b) = y (a - b)$

Rewrite the expression.

$x a b = y (a - b)$

Simplify the right side.

Apply the distributive property.

$x a b = y a + y (- b)$

Rewrite using the commutative property of multiplication.

$x a b = y a - y b$

Solve the equation.

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

$x a b - y a = - y b$

Factor $a$ out of $x a b - y a$ .

Factor $a$ out of $x a b$ .

$a (x b) - y a = - y b$

Factor $a$ out of $- y a$ .

$a (x b) + a (- y) = - y b$

Factor $a$ out of $a (x b) + a (- y)$ .

$a (x b - y) = - y b$

Divide each term in $a (x b - y) = - y b$ by $x b - y$ and simplify.

Divide each term in $a (x b - y) = - y b$ by $x b - y$ .

$\frac{a (x b - y)}{x b - y} = \frac{- y b}{x b - y}$

Simplify the left side.

Cancel the common factor of $x b - y$ .

Cancel the common factor.

$\frac{a (x b - y)}{x b - y} = \frac{- y b}{x b - y}$

Divide $a$ by $1$ .

$a = \frac{- y b}{x b - y}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{y b}{x b - y}$

Solve for a y=x((ab)/(a-b))

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