Answer
$a\ne -1$
$\frac{a+1}{5}$
Work Step by Step
To find excluded values, we look at the denominator and find the values that would make it zero. To do this, we can set the denominator equal to zero and solve.
$5a + 5 = 0$
$5a +5=0 -5$ Subtract 5 from each side
$\frac{5}{5}a = \frac{-5}{5}$ Divide each side by 5
$a = -1$ Simplify
Therefore, $a\ne-1$, therefore -1 is our excluded value.
To simplify the expression, we need to factor the numerator and denominator.
$\frac{a^2+2a+1}{5a+5} = \frac{(a+1)(a+1)}{5(a+1)}$
Now we can divide out the common factor of $(a+1)$
$\frac{(a+1)(a+1)}{5(a+1)} = \frac{a+1}{5}$
