1/a-1/b
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a/b-b/a
please simplify
triple decker fraction
you will have a common denominator of ab for the top and a common denominator of ab for the bottom, so they will cancel
remember that to divide one fraction by another, you multiply the first by the reciprocal of the second
after that I see a difference of square at the bottom
I see an answer of -1/(a+b)
see if that is what you get
To simplify the given expression, we can start by finding a common denominator for both the numerator and denominator.
For the numerator, we have 1/a - 1/b. The common denominator for these fractions will be ab.
So, rewriting the numerator with the common denominator, we get (b - a)/(ab).
Now, let's work on the denominator, which is a/b - b/a. Again, the common denominator for these fractions will be ab.
Rewriting the denominator with the common denominator, we get (a^2 - b^2)/(ab).
Now, we can simplify the expression by dividing the numerator by the denominator:
[(b - a)/(ab)] / [(a^2 - b^2)/(ab)]
To divide one fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction:
[(b - a)/(ab)] * [(ab)/(a^2 - b^2)]
Cancelling out the common factors of ab, we get:
(b - a)/(a^2 - b^2)
Recognizing that (a^2 - b^2) is a difference of squares, we can further simplify:
(b - a)/[(a + b)(a - b)]
Therefore, the simplified form of the expression is -1/(a + b).