Question

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

Answer 1

`y/[2y] + [y+2]/y`

`=[y+2(y+2)]/[2y]`

`=[y+2y+4]/[2y]`

`=[3y+4]/[2y]`

Answer 2

`\frac{3y+4}{2y}`

Explanation:

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

`\frac{y}{2y}+\frac{2(y+2)}{2y} = \frac{y+2(y+2)}{2y} = \frac{y+2y+4}{2y}=\frac{3y+4}{2y}`

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

`\frac{3y+4}{2y} = \frac{3cancel(y)}{2cancel(y)}+\frac{cancel(4)^2}{cancel(2)y} = \frac{3}[2}+\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!