# How do you simplify and restricted value of (y^2-16)/(y^2+16)?

Aug 27, 2017

See a solution process below:

#### Explanation:

We can simplify the numerator using this special case for quadratics:

${\textcolor{red}{a}}^{2} - {\textcolor{b l u e}{b}}^{2} = \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) \left(\textcolor{red}{a} - \textcolor{b l u e}{b}\right)$

$\frac{{\textcolor{red}{y}}^{2} - {\textcolor{b l u e}{16}}^{2}}{{y}^{2} + 16} = \frac{\left(\textcolor{red}{y} + \textcolor{b l u e}{4}\right) \left(\textcolor{red}{y} - \textcolor{b l u e}{4}\right)}{{y}^{2} + 16}$

Because we cannot divide by $0$, the restricted value is:

${y}^{2} + 16 \ne 0$

However, because a number squared will always be non-negative (0 or positive), the ${y}^{2}$ will always be greater than or equal to $0$.

And then, adding $16$ to this will give a number greater than or equal to 16.

Therefore, ${y}^{2} + 16$ can never be $0$ so there are no restrictions.