SOLUTION: f(x)=1-x^2 and g(x)=1-x. Find (f/g)(x)

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Question 148161: f(x)=1-x^2 and g(x)=1-x. Find (f/g)(x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28f%2Fg%29%28x%29=%28f%28x%29%29%2F%28g%28x%29%29 Start with the given property


%28f%28x%29%29%2F%28g%28x%29%29=%281-x%5E2%29%2F%281-x%29 Plug in f%28x%29=1-x%5E2 and g%28x%29=1-x


%28f%28x%29%29%2F%28g%28x%29%29=%28%281-x%29%281%2Bx%29%29%2F%281-x%29 Factor the numerator.


Highlight the common terms.


%28f%28x%29%29%2F%28g%28x%29%29=%28cross%28%281-x%29%29%281%2Bx%29%29%2Fcross%28%281-x%29%29 Cancel out the common terms.


%28f%28x%29%29%2F%28g%28x%29%29=1%2Bx Simplify


%28f%28x%29%29%2F%28g%28x%29%29=x%2B1 Rearrange the terms.