Question

Find the lowest common denominator of the following fractions. 5/n-2 and n+2/n^2-4

Answer 1

The denominator of the second fraction is the difference of squares, so can be factored using the formula for that.
  (n^2 -4) = (n -2)(n +2)

Now, you will note that the second fraction has a numerator that is equal to one of the factors in the denominator. In other words, the whole fraction can be simplified to ...
  (n +2)/((n +2)(n -2)) = 1/(n -2) . . . . with the restriction n≠-2

This reduced form of the fraction has the same denominator as the first fraction, so you can say that the lowest common denominator is that: (n -2).


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If there is some reason you don't want to reduce the second fraction, the lowest common denominator will be (n -2)(n +2).