# How do you simplify and find the excluded value of  (9y + 8) / (y) ?

Jun 1, 2017

See a solution process below:

#### Explanation:

Because we cannot divide by $0$, the excluded value is $y = 0$.

To simplify, we can split the fraction and cancel common terms as follows:

$\frac{9 y + 8}{y} \implies$

$\frac{9 y}{y} + \frac{8}{y} \implies$

$\frac{9 \textcolor{red}{\cancel{\textcolor{b l a c k}{y}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{y}}}} + \frac{8}{y} \implies$

$9 + \frac{8}{y}$

Jun 1, 2017

$9 + \frac{8}{y}$

Excluded value $\to y = 0$

#### Explanation:

This is the same as: $\text{ "(9y)/y+8/y " "->" } 9 + \frac{8}{y}$

This 'expression' (no equals sign) becomes undefined at $y = 0$ thus $y = 0$ is an excluded value giving rise to an asymptote.

As $y$ becomes increasingly positive or negative then $\frac{8}{y}$ tend to 0. So we end up with just 9