SOLUTION: Need help once again, can't seem to figure this out. Let h and g be two functions defined by h(x)=(5+x)(-6+x) g(x)=2-x for any real number x. Find h/g(3) and then find al

Algebra ->  Rational-functions -> SOLUTION: Need help once again, can't seem to figure this out. Let h and g be two functions defined by h(x)=(5+x)(-6+x) g(x)=2-x for any real number x. Find h/g(3) and then find al      Log On


   

Question 528003: Need help once again, can't seem to figure this out.
Let h and g be two functions defined by
h(x)=(5+x)(-6+x)
g(x)=2-x
for any real number x.
Find h/g(3) and then find all values that are NOT in the domain of h/g. If there is more than one value, separate them with commas.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
h(x)=(5+x)(-6+x)

h(3)=(5+3)(-6+3)

h(3)=(8)(-3)

h(3) = -24
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g(x)=2-x

g(3)=2-3

g(3) = -1

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(h/g)(x) = (h(x))/(g(x))


(h/g)(3) = (h(3))/(g(3))


(h/g)(3) = -24/(-1)


(h/g)(3) = 24

======================================

Since you CANNOT divide by zero, this means that the denominator g(x) cannot be zero.

If it were, then g(x) = 0 would mean that 2-x = 0 and that x = 2


So x = 2 makes the denominator zero. So we must exclude that from the domain.



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