Please Help! I really don't understand anything in this Unit. (11/2/18)

$\dfrac{b^2 + 10b + 24}{10b^2+40b} = \\ \dfrac{ b^2 + 10 b + 24}{10b(b+4)} = \\ \dfrac{(b+6)(b+4)}{10b(b+4)}=\\ \dfrac{b+6}{10b}$

The only excluded value is 

$b=0$

The numerator is a polynomial......so any real number  b will "work"

We only have to worry about the  denominator  being 0

To find which values make this so we have

10b^2 + 40b  =  0      factor

10b ( b + 4)  =  0

So  either   10b  = 0   and b  = 0   or  b + 4  = 0   and b  = -4

So...the excluded values  are   0  and - 4

The simplified rational function is  just as Rom found....