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Help on Simplifying Complex Fractions?
x/x+1 - 1/x
---------------- -over-
x/x+1 +1/x
1 Answer
- 10 years agoFavorite Answer
I sometimes find it's easier to think about if I write it out the long way like,
[x/(x+1) - 1/x] ÷ [x/(x+1) + 1/x].
Find common denominator for both sides of division operation (you can cross multiply here),
[x^2 - (x+1)]/[x(x+1)] ÷ [x^2 + (x+1)]/[x(x+1)].
Simplifying and taking the reciprocal of the right part,
(x^2 - x - 1)/[x(x+1)] • [x(x+1)]/(x^2 + x + 1).
Now, the x(x+1) can be cancelled from the numerator and denominator leaving,
(x^2 - x - 1)/(x^2 + x + 1) as the answer.
