SOLUTION: If f(x)=1/x and g(x)=1/x^3, find (f+g)(x). Is it x^2+1/x^2, x^2+1/x^2, 1,or 1/2x^4 thank-you..

Algebra ->  Functions -> SOLUTION: If f(x)=1/x and g(x)=1/x^3, find (f+g)(x). Is it x^2+1/x^2, x^2+1/x^2, 1,or 1/2x^4 thank-you..      Log On


   

Question 202895: If f(x)=1/x and g(x)=1/x^3, find (f+g)(x). Is it x^2+1/x^2, x^2+1/x^2, 1,or 1/2x^4 thank-you..
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(f+g)(x) is simply shorthand for f(x) + g(x). So (f+g)(x) in your problem is 1/x + 1/x^3. Since this is not one of the listed answers we will have to add the fractions to see what it looks like then.

To add fractions:
  1. Factor each denominator
  2. Multiply the numerator and denominator of each fraction by whatever is needed to make each denominator the same
  3. Simplify (multiply) the numerators but leave the denominators factored
  4. Add the numerators of the fractions
  5. Factor the new numerator, if possible
  6. If the denominator is still factored, multiply it out.

We'll use this on:
1%2Fx+%2B+1%2F%28x%5E3%29
Factor the denominators:
1%2Fx+%2B+1%2F%28x%2Ax%2Ax%29
Multiply the top and bottom of each fraction, as needed, to get the denominators the same. It takes some practice to develop an "eye" for how to do this. I hope that it is clear that if the top and bottom of the first fraction is multiplied by (x*x) then its denominator would be the same as the denominator in the second fraction:
%28%28x%2Ax%29%2F%28x%2Ax%29%29%2A%281%2Fx%29+%2B+1%2F%28x%2Ax%2Ax%29
Multiply the numerator(s):
%28x%5E2%29%2F%28x%2Ax%2Ax%29+%2B+1%2F%28x%2Ax%2Ax%29
Add the fractions:
%28x%5E2+%2B+1%29%2F%28x%2Ax%2Ax%29
Factor the numerator. This numerator will not factor.
Cancel common factors. There are no common factors
Multiply out the denominator.
%28x%5E2%2B1%29%2F%28x%5E3%29
This is (f+g)(x). Since it does not match any of the answers you've provided, I can only guess that either you mistyped the answers (the first two are exactly the same!?) or there is an error in the answers provided in your source of the problem.