Simplify:
(1)/(z-4)-(1)/z+4
To simplify the expression (1)/(z-4) - (1)/(z+4), we need to find a common denominator for the two fractions. The common denominator is (z-4)(z+4), as it includes both z-4 and z+4.
Now, let's rewrite the fractions using the common denominator:
(1)/(z-4) - (1)/(z+4) = [(1)(z+4)]/[(z-4)(z+4)] - [(1)(z-4)]/[(z-4)(z+4)]
Simplifying the numerators, we get:
(z+4) - (z-4) = z + 4 - z + 4
Combining like terms, we have:
z - z + 4 + 4 = 8
Therefore, the simplified expression is 8/(z^2 - 16).