How do you simplify y/(2y)+ (y+2)/y?

Jun 14, 2018

$\frac{y}{2 y} + \frac{y + 2}{y}$

$= \frac{y + 2 \left(y + 2\right)}{2 y}$

$= \frac{y + 2 y + 4}{2 y}$

$= \frac{3 y + 4}{2 y}$

Jun 14, 2018

$\setminus \frac{3 y + 4}{2 y}$

Explanation:

If you multiply and divide by $2$ the second fraction we get

$\setminus \frac{y}{2 y} + \setminus \frac{2 \left(y + 2\right)}{2 y} = \setminus \frac{y + 2 \left(y + 2\right)}{2 y} = \setminus \frac{y + 2 y + 4}{2 y} = \setminus \frac{3 y + 4}{2 y}$

If you prefer, you can break the fraction in two fraction by writing

$\setminus \frac{3 y + 4}{2 y} = \setminus \frac{3 \cancel{y}}{2 \cancel{y}} + \setminus \frac{{\cancel{4}}^{2}}{\cancel{2} y} = \setminus \frac{3}{2} + \setminus \frac{2}{y}$.

It depends on your idea of "simplifying", as far as I know there is no standard definition for that term. Let me know if I'm wrong!