perform indicated operation then express in lowest terms?

Question

[1/t+1] - [1/t-1]

Answer 1

Assuming you didn't miss some parentheses (I bet you did....):

1/t + 1 - (1/t - 1) =
1/t + 1 - 1/t + 1 = 1 + 1 = 2

Answer 2

AS in arithmetic, you need to get the fractions with the same common denominator. It is (t+1)(t-1)

Multiply numerator and denominator of each fraction by the factor needed.

(t-1)/(t+1)(t-1) - (t+1)/((t-1)(t+1)

now write it as a single fraction adn keep the numerators in the parentheses

[(t-1)-(t+1)]/(t+1)(t-1)

simplify the numerator by removing ( ) and combining like terms

(t-1-t-1)/(t+1)(t-1)
-2/(t+1)(t-1)

this is as far as you can simplify because there are no common factors.