Solve for y x=1/(y+2)

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

Step 1

Rewrite the equation as $\frac{1}{y + 2} = x$ .

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

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.

$y + 2, 1$

Remove parentheses.

$y + 2, 1$

The LCM of one and any expression is the expression.

$y + 2$

Step 3

Multiply each term in $\frac{1}{y + 2} = x$ by $y + 2$ to eliminate the fractions.

Multiply each term in $\frac{1}{y + 2} = x$ by $y + 2$ .

$\frac{1}{y + 2} (y + 2) = x (y + 2)$

Simplify the left side.

Cancel the common factor of $y + 2$ .

Cancel the common factor.

$\frac{1}{y + 2} (y + 2) = x (y + 2)$

Rewrite the expression.

$1 = x (y + 2)$

Simplify the right side.

Apply the distributive property.

$1 = x y + x \cdot 2$

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

$1 = x y + 2 x$

Step 4

Solve the equation.

Rewrite the equation as $x y + 2 x = 1$ .

$x y + 2 x = 1$

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

$x y = 1 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $- 2$ by $1$ .

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

Solve for y x=1/(y+2)

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