SOLUTION: Need help with solving problem: Given f(x)=1/x and (f/g)(x)=(x-2)/(x^2+7x), find the function g.

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Question 964496: Need help with solving problem: Given f(x)=1/x and (f/g)(x)=(x-2)/(x^2+7x), find the function g.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Dividing function f by function g must result in %28x-2%29%2F%28x%5E2%2B7x%29.

I use here g for g(x), the unknown function.

f%2Fg=%281%2Fx%29%2Fg=%28x-2%29%2F%28x%5E2%2B7x%29

1%2F%28x%2Ag%29=%28x-2%29%2F%28x%5E2%2B7x%29

xg=%28x%5E2%2B7x%29%2F%28x-2%29

highlight%28g=%28x%5E2%2B7x%29%2F%28x%28x-2%29%29%29, and do not simplify this any further, because doing so will change part of the meaning of the function g. g(x) currently is shown to have vertical asymtptote for x=0, and for x=2.