SOLUTION: Find (f+g)(x), (f-g)(x), (f*g)(x)and (f/g)(x) for each f(x) and g(x) 2.f(x)=8x^2 G(x)=1/x^2

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Find (f+g)(x), (f-g)(x), (f*g)(x)and (f/g)(x) for each f(x) and g(x) 2.f(x)=8x^2 G(x)=1/x^2      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 188989This question is from textbook algebra2
: Find (f+g)(x), (f-g)(x), (f*g)(x)and (f/g)(x) for each f(x) and g(x)
2.f(x)=8x^2
G(x)=1/x^2This question is from textbook algebra2

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Note: for every example, x%3C%3E0 (to avoid division by zero)


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


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


8x%5E2%2B1%2Fx%5E2 Plug in f%28x%29=8x%5E2 and g%28x%29=1%2Fx%5E2


8x%5E2%28x%5E2%2Fx%5E2%29%2B1%2Fx%5E2 Multiply the first term by x%5E2%2Fx%5E2 (to get the denominators the same.


8x%5E4%2Fx%5E2%2B1%2Fx%5E2 Multiply


%288x%5E4%2B1%29%2Fx%5E2 Combine the fractions.


So %28f%2Bg%29%28x%29=%288x%5E4%2B1%29%2Fx%5E2


-------------------------------------------------------

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


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


8x%5E2-1%2Fx%5E2 Plug in f%28x%29=8x%5E2 and g%28x%29=1%2Fx%5E2


8x%5E2%28x%5E2%2Fx%5E2%29-1%2Fx%5E2 Multiply the first term by x%5E2%2Fx%5E2 (to get the denominators the same.


8x%5E4%2Fx%5E2-1%2Fx%5E2 Multiply


%288x%5E4-1%29%2Fx%5E2 Combine the fractions.


So %28f-g%29%28x%29=%288x%5E4-1%29%2Fx%5E2

--------------------------------------------------------

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


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


%288x%5E2%29%281%2Fx%5E2%29 Plug in f%28x%29=8x%5E2 and g%28x%29=1%2Fx%5E2


8x%5E2%2Fx%5E2 Combine the fractions.


8 Simplify (the x%5E2 terms cancel out)


So %28f%2Ag%29%28x%29=8


--------------------------------------------------------

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


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


%288x%5E2%29%2F%281%2Fx%5E2%29 Plug in f%28x%29=8x%5E2 and g%28x%29=1%2Fx%5E2


%288x%5E2%29%28x%5E2%2F1%29 Multiply by the reciprocal of the second fraction.


%288x%5E2%2Ax%5E2%29%2F1 Combine the fractions.


8x%5E4%2F1 Multiply (add the exponents)


8x%5E4 Reduce


So %28f%2Fg%29%28x%29=8x%5E4