(ii) Find the set of real values of x for which |(x+3)/(x-5)| = (x+3)/(x-5).

Here are the solutions to the questions:

1. (ii) Find the set of real values of $x$ for which $\left|\frac{x+3}{x-5}\right| = \frac{x+3}{x-5}$.
The condition $|A| = A$ implies that $A \ge 0$.
Therefore, we need to solve the inequality $\frac{x+3}{x-5} \ge 0$.

Step 1: Identify critical points where the numerator or denominator is zero.
$x+3 = 0 \implies x = -3$
$x-5 = 0 \implies x = 5$ (Note: $x \ne 5$ because the denominator cannot be zero).

Step