Consider the function

$f(x)=\{\begin{array}{ccc}\frac{|x-4|}{x^2-16}& if& x4\\ \frac{1}{x+a}& if& x=4\end{array}$

a$)$ Suppose first that

In this case, simplify the following expression so that it does not involve an absolute value:

$\frac{|x-4|}{x^2-16}=$

$$

b$)$ Compute the following limit$.$

$\underset{x{4}^{-}}{lim}f(x)=$

c$)$ Now suppose that $x>4.$

In this case, simplify the following expression so that it does not involve an absolute value:

$\frac{|x-4|}{x^2-16}=$

$$

d$)$ Compute the following limit$.$

$\underset{x{4}^{+}}{lim}f(x)=$

e$)$ If possible, find the value of a such that $f$ is continuous at $x=4.$ If there is no value, write empty.

$a=$

Need the answer for A and C