Solve for y x=4/(2-y)

$x = \frac{4}{2 - y}$

Step 1

Rewrite the equation as $\frac{4}{2 - y} = x$ .

$\frac{4}{2 - y} = x$

Step 2

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.

$2 - y, 1$

Remove parentheses.

$2 - y, 1$

The LCM of one and any expression is the expression.

$2 - y$

Step 3

Multiply each term in $\frac{4}{2 - y} = x$ by $2 - y$ to eliminate the fractions.

Multiply each term in $\frac{4}{2 - y} = x$ by $2 - y$ .

$\frac{4}{2 - y} (2 - y) = x (2 - y)$

Simplify the left side.

Cancel the common factor of $2 - y$ .

Cancel the common factor.

$\frac{4}{2 - y} (2 - y) = x (2 - y)$

Rewrite the expression.

$4 = x (2 - y)$

Simplify the right side.

Apply the distributive property.

$4 = x \cdot 2 + x (- y)$

Reorder.

Move $2$ to the left of $x$ .

$4 = 2 \cdot x + x (- y)$

Rewrite using the commutative property of multiplication.

$4 = 2 x - x y$

Step 4

Solve the equation.

Rewrite the equation as $2 x - x y = 4$ .

$2 x - x y = 4$

Subtract $2 x$ from both sides of the equation.

$- x y = 4 - 2 x$

Divide each term in $- x y = 4 - 2 x$ by $- 1 x$ and simplify.

Divide each term in $- x y = 4 - 2 x$ by $- 1 x$ .

$\frac{- x y}{- 1 x} = \frac{4}{- 1 x} + \frac{- 2 x}{- 1 x}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x y}{x} = \frac{4}{- 1 x} + \frac{- 2 x}{- 1 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{4}{- 1 x} + \frac{- 2 x}{- 1 x}$

Divide $y$ by $1$ .

$y = \frac{4}{- 1 x} + \frac{- 2 x}{- 1 x}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4}{x} + \frac{- 2 x}{- 1 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$y = - \frac{4}{x} + \frac{- 2 x}{- 1 x}$

Rewrite the expression.

$y = - \frac{4}{x} + \frac{- 2}{- 1}$

Move the negative one from the denominator of $\frac{- 2}{- 1}$ .

$y = - \frac{4}{x} - 1 \cdot - 2$

Rewrite $- 1 \cdot - 2$ as $- - 2$ .

$y = - \frac{4}{x} - - 2$

Multiply $- 1$ by $- 2$ .

$y = - \frac{4}{x} + 2$

Solve for y x=4/(2-y)

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