A-b/b - a/a+b ; 2x/y • x+1/y²; x²-1/x : x+1/2

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Let's simplify each of these expressions one by one:

(a-b)/b - a/(a+b)
To combine these fractions, we need to find a common denominator, which in this case is (a+b)b.
= [(a-b)(a+b) - ab]/[(a+b)b]
= [a^2 - b^2 - ab]/[(a+b)b]

2x/y • x+1/y^2
Multiplying these fractions together gives us:
= 2x(x+1)/(y*y^2)
= 2x(x+1)/y^3
= 2x^2 + 2x/y^3

(x^2 - 1)/(x) : (x+1)/2
To divide these fractions, we need to invert and multiply the second fraction:
= (x^2 - 1)/(x) * (2/(x+1))
= 2(x^2 - 1)/(x(x+1))
= 2(x-1)(x+1)/(x(x+1))
= 2(x-1)/x

I hope this helps! Let me know if you have any further questions.