How to simplify this fraction

Question

It's embarrassing, but I need help solving this one... Need some refresher course for algebra.

$$ \frac y{y+\sqrt y} $$

Answer 1

Multiply by the conjugate of the denominator $y-\sqrt y$, $$\frac{y}{y+\sqrt y} \cdot \frac{y-\sqrt y}{y-\sqrt y} = \frac{y^2 -y\sqrt y}{y^2 - y} = \frac{y(y-\sqrt y)}{y (y-1)} =\frac{y-\sqrt y}{y-1}$$

Answer 2

Using the fact that $y = \sqrt{y}^2$, you could write this as

$$\frac{\sqrt{y}^2}{\sqrt{y}^2 + \sqrt{y}} = \frac{\sqrt y}{\sqrt y + 1}$$

Alternatively, multiply top and bottom by $y - \sqrt{y}$ and simplify.