-8/3z-1+9/3z+1=5/9z^2-1

Assuming this is correct interpretation:

-8/(3z-1) + 9/(3z+1) = 5/(9z^2-1)

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

Multiply both sides by (3z-1)(3z+1):

-8(3z+1) +9(3z-1) = 5

-24z - 8 + 27z - 9 = 5

3z = 22

z = 22/3

-8/(3z-1) + 9/(3z+1) = 5/(9z^2-1)

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

Multiply both sides by (3z-1)(3z+1):

-8(3z+1) +9(3z-1) = 5

-24z - 8 + 27z - 9 = 5

3z = 22

z = 22/3

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