How do you solve for Y? when the equation looks like this? x=y/y+1? The answer is y= x/x-1 but I don't know how they got there. Thanks

Question

anonymous · Answer

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

anonymous · Answer

answer is : $$Y=\frac{ x }{ 1-x }$$

cruffo · Answer

multiply both sides of the equation by the denominator (y+1):
$$ \large (y+1)\left( x\right) = (y+1)\left(\frac{y}{y+1} \right)$$
Then simplify:
$$\large xy + x = y$$
gather on the left all terms that have a y in them:
$$\large xy - y = -x$$
and factor out y:
$$\large y(x-1) = -x$$
Divide both sides by (x-1):
$$\large y = \frac{-x}{x-1}$$
Note that $\dfrac{-a}{b}$ is the same as $\dfrac{a}{-b}$, so a little rewritting...
$$\large y = \frac{-x}{x-1} = \frac{x}{-(x-1)} = \frac{x}{-x+1} = \frac{x}{1-x}$$

anonymous · Answer

I feel dumb now! Thanks!

precal · Answer

cruffo is correct, 
@en28so you just need a little thing called "experience" and then you will be an expert at doing these types of problems
Welcome to Open Study :)