Make y the subject of the formula

To make $y$ the subject of the formula $x = \frac{y}{y+1}$, follow these steps:

Step 1: Multiply both sides of the equation by $(y+1)$ to eliminate the denominator. $x(y+1) = y$

Step 2: Distribute $x$ on the left side. $xy + x = y$

Step 3: Gather all terms containing $y$ on one side of the equation and terms without $y$ on the other side. Subtract $xy$ from both sides: $x = y - xy$

Step 4: Factor out $y$ from the terms on the right side. $x = y(1 - x)$

Step 5: Divide both sides by $(1 - x)$ to isolate $y$. $\frac{x}{1 - x} = y$

So, $y$ as the subject of the formula is: y = \frac{x{1 - x}}