Find all values of z such that 2/z + 5 = 5/z - 4 - 2/z - 8
Let \(x = \frac 1z\). Then \(2x + 5 = 5x - 4 - 2x - 8 \implies 2x + 5 = 3x - 12 \implies 5 = x - 12 \implies x = 17\). Hence, \(z = \boxed{\frac 1{17}}\).
