SOLUTION: (3x^-1)/3 +4/3

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Question 380175: (3x^-1)/3 +4/3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E%28-1%29%29%2F3+%2B4%2F3
Since x%5E%28-1%29+=+1%2Fx this becomes:
%283%281%2Fx%29%29%2F3+%2B4%2F3
To simplify the fraction within a fraction we multiply the numerator and denominator of the "big" fraction by the lowest common denominator (LCD) of the "little" denominators. Since there is only one "little" denominator the LCD is simply that denominator, x:
%28%283%281%2Fx%29%29%2F3%29%28x%2Fx%29+%2B4%2F3
In the numerator the x's cancel, leaving a 3. In the denominator we get 3x:
3%2F%283x%29+%2B+4%2F3
To add these fractions we need common denominators. The LCD of these two is 3x. So we multiply the numerator and denominator of the second fraction by x/x:
3%2F%283x%29+%2B+%284%2F3%29%28x%2Fx%29
3%2F%283x%29+%2B+%284x%29%2F%283x%29
Now we can add:
%283+%2B+4x%29%2F%283x%29
This fraction cannot be reduced. (The x's and the 3's are not factors and only factors can be canceled!) So we are finished.