SOLUTION: determine the reciprocal of 1 over f plus 1 over g 1/f + 1/g. for what values of f and g is the reciprocal defined?

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Question 220242: determine the reciprocal of 1 over f plus 1 over g
1/f + 1/g.
for what values of f and g is the reciprocal defined?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: f%3C%3E0 or g%3C%3E0


1%2Ff+%2B+1%2Fg Start with the given expression.


g%2F%28fg%29+%2B+1%2Fg Multiply the first fraction by g%2Fg


g%2F%28fg%29+%2B+f%2F%28fg%29 Multiply the second fraction by f%2Ff


%28g%2Bf%29%2F%28fg%29 Combine the fractions.


%28fg%29%2F%28g%2Bf%29 Take the reciprocal of the fraction.


Since g%2Bf%3C%3E0 (to avoid dividing by zero), this means f%3C%3E-g.


So the reciprocal of 1%2Ff+%2B+1%2Fg is defined whenever f%3C%3E-g.