(2ab/a²-b²+a-b/2(a+b))×2a/a+b-b/a-b

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Let's simplify the given expression step by step:

(2ab/a²-b²+a-b/2(a+b)) = (2ab/a² - b² + a - b/2(a + b))

Factoring out the common factor in each term:
= 2ab/(a - b)(a + b) + (a - b)/(2(a + b))

Multiplying the first term by 2a/(a + b) and the second term by (a - b)/(a - b):
= 2ab 2a/[(a - b)(a + b)] + (a - b) (a - b)/[2(a + b)(a - b)]
= 4a²b/(a² - b²) + (a² - 2ab + b²)/[2(a² - b²)]

Simplifying further:
= 4a²b/(a² - b²) + [(a - b)²]/[2(a² - b²)]
= 4a²b/(a² - b²) + (a² - 2ab + b²)/(2a² - 2b²)
= 4a²b/(a² - b²) + [a² - 2ab + b²]/[2(a² - b²)]

Therefore, the simplified form of the given expression is:
(4a²b/(a² - b²) + [a² - 2ab + b²]/[2(a² - b²)])