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

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

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

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

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.

$y + 1, 1$

Remove parentheses.

$y + 1, 1$

The LCM of one and any expression is the expression.

$y + 1$

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

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

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

Simplify the left side.

Cancel the common factor of $y + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$y = x (y + 1)$

Simplify the right side.

Apply the distributive property.

$y = x y + x \cdot 1$

Multiply $x$ by $1$ .

$y = x y + x$

Solve the equation.

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

$y - x y = x$

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

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

$y \cdot 1 - x y = x$

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

$y \cdot 1 + y (- x) = x$

Factor $y$ out of $y \cdot 1 + y (- x)$ .

$y (1 - x) = x$

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

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

$\frac{y (1 - x)}{1 - x} = \frac{x}{1 - x}$

Simplify the left side.

Cancel the common factor of $1 - x$ .

Cancel the common factor.

$\frac{y (1 - x)}{1 - x} = \frac{x}{1 - x}$

Divide $y$ by $1$ .

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