(1/а-1/b):b^2-a^2/ab^2

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вопрос

To simplify the expression (1/a - 1/b), we need to find a common denominator and then combine the fractions.

The common denominator for the fractions 1/a and 1/b is ab. So, we can rewrite the expression as:
(1/a)(b/b) - (1/b)(a/a)
= b/ab - a/ab
= (b - a)/ab

Now, to simplify the expression (b^2 - a^2)/(ab^2), we can factor the numerator as the difference of squares:
(b^2 - a^2) = (b + a)(b - a)

Therefore, the simplified expression becomes:
(b + a)(b - a)/(ab^2)

So, the simplified expression of (1/a - 1/b) : (b^2 - a^2)/ab^2 is:
(b + a)(b - a)/(ab^2) : (b + a)(b - a)/(ab^2)
= 1:1