# How do you simplify and find the restrictions for (y-3)/(y+5)?

May 4, 2016

restriction: $y \ne - 5$

#### Explanation:

The given expression is already simplified and cannot be simplified any further.

To find the restriction, recall that in any fraction, the denominator must not equal to $0$. In the given fraction,

$\frac{y - 3}{y + 5}$

the denominator is expressed as a variable plus a constant. When setting the denominator to equal to $0$, you are solving for the value of $y$ that will produce a denominator or $0$. The $y$ value would be your restriction.

Thus,

$y + 5 = 0$

$y + 5 \textcolor{w h i t e}{i} \textcolor{red}{- 5} = 0 \textcolor{w h i t e}{i} \textcolor{red}{- 5}$

$y = - 5$

restriction: $\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y \ne - 5} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

To check your answer, you can plug in $y = - 5$ into the given expression to check if the denominator equals $0$. If it does, then you know the restriction is correct.

Plugging in $y = - 5$,

$\frac{y - 3}{y + 5}$

$= \frac{- 5 - 3}{- 5 + 5}$

$= - \frac{8}{0}$

undefined

$\therefore$, the restriction is correct.