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#1**+1 **

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

The only excluded value is

\(b=0\)

.Rom Nov 2, 2018

#2**+1 **

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....

CPhill Nov 3, 2018