SOLUTION: Find (f+g)(x), (f-g)(x), (f*g)(x) snd (f/g)(x) for each f(x) and g(x) 3. f(x)= x^2+7x+12 g(x)= x^2-9

Algebra ->  Rational-functions -> SOLUTION: Find (f+g)(x), (f-g)(x), (f*g)(x) snd (f/g)(x) for each f(x) and g(x) 3. f(x)= x^2+7x+12 g(x)= x^2-9      Log On


   

Question 188930This question is from textbook algebra2
: Find (f+g)(x), (f-g)(x), (f*g)(x) snd (f/g)(x) for each f(x) and g(x)

3. f(x)= x^2+7x+12
g(x)= x^2-9 This question is from textbook algebra2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28f%2Bg%29%28x%29 Start with the given expression.


f%28x%29%2Bg%28x%29 Expand


%28x%5E2%2B7x%2B12%29%2B%28x%5E2-9%29 Plug in f%28x%29=+x%5E2%2B7x%2B12 and g%28x%29=+x%5E2-9


2x%5E2%2B7x%2B3 Combine like terms.


So %28f%2Bg%29%28x%29=2x%5E2%2B7x%2B3


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%28f-g%29%28x%29 Start with the given expression.


f%28x%29-g%28x%29 Expand


%28x%5E2%2B7x%2B12%29-%28x%5E2-9%29 Plug in f%28x%29=+x%5E2%2B7x%2B12 and g%28x%29=+x%5E2-9


x%5E2%2B7x%2B12-x%5E2%2B9 Distribute


7x%2B21 Combine like terms.


So %28f-g%29%28x%29=7x%2B21


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%28f%2Ag%29%28x%29 Start with the given expression.


f%28x%29%2Ag%28x%29 Expand


%28x%5E2%2B7x%2B12%29%2A%28x%5E2-9%29 Plug in f%28x%29=+x%5E2%2B7x%2B12 and g%28x%29=+x%5E2-9



%28x%5E2-9%29%28x%5E2%2B7x%2B12%29 Rearrange the terms.


x%5E2%28x%5E2%2B7x%2B12%29-9%28x%5E2%2B7x%2B12%29 Expand. Note: %28a%2Bb%29%28c%2Bd%2Be%29=a%28c%2Bd%2Be%29%2Bb%28c%2Bd%2Be%29


x%5E2%28x%5E2%29%2Bx%5E2%287x%29%2Bx%5E2%2812%29-9%28x%5E2%29-9%287x%29-9%2812%29 Distribute


x%5E4%2B7x%5E3%2B12x%5E2-9x%5E2-63x-108 Multiply


x%5E4%2B7x%5E3%2B3x%5E2-63x-108 Combine like terms.


So %28f%2Ag%29%28x%29=x%5E4%2B7x%5E3%2B3x%5E2-63x-108


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%28f%2Fg%29%28x%29 Start with the given expression.


f%28x%29%2Fg%28x%29 Expand


%28x%5E2%2B7x%2B12%29%2F%28x%5E2-9%29 Plug in f%28x%29=+x%5E2%2B7x%2B12 and g%28x%29=+x%5E2-9


%28%28x%2B4%29%28x%2B3%29%29%2F%28x%5E2-9%29 Factor x%5E2%2B7x%2B12 to get %28x%2B4%29%28x%2B3%29.


%28%28x%2B4%29%28x%2B3%29%29%2F%28%28x-3%29%28x%2B3%29%29 Factor x%5E2-9 to get %28x-3%29%28x%2B3%29.


%28%28x%2B4%29highlight%28%28x%2B3%29%29%29%2F%28%28x-3%29highlight%28%28x%2B3%29%29%29 Highlight the common terms.


%28%28x%2B4%29cross%28%28x%2B3%29%29%29%2F%28%28x-3%29cross%28%28x%2B3%29%29%29 Cancel out the common terms.


%28x%2B4%29%2F%28x-3%29 Simplify.



So %28f%2Fg%29%28x%29=%28x%2B4%29%2F%28x-3%29 where x%3C%3E-3 or x%3C%3E3


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