For the expression: (a+b/b - a/a+b) : (a+/a - b/a+b) Find the domain. AND Prove that for all admissible values of a, the value of the expression (5/a+1 - 3/a-1 + 6/a^2-1) * a+1/2 does not depend on a.

Step-by-step explanation:

((a+b) / b - a / (a+b)) : ((a+b) / a - b / (a+b))

To find the domain, remember that any denominators can't be 0.

b ≠ 0

a + b ≠ 0

a ≠ 0

(5 / (a+1) - 3 / (a-1) + 6 / (a²-1)) * (a+1) / 2

Distribute the a+1.

(5 - 3 (a+1) / (a-1) + 6 / (a-1)) / 2

Factor out 1 / (a-1).

(5 (a-1) - 3 (a+1) + 6) / (2 (a-1))

Simplify.

(5a - 5 - 3a - 3 + 6) / (2a-2)

(2a-2) / (2a-2)

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