Question

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.

Answer 1

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)

1