To make x the subject of the given relation, we need to isolate x on one side of the equation.
First, we can simplify the expression by finding the common denominator of the two fractions in the numerator:
(1 + ax)/(1 - ax) = (1 - ax + ax + a^2x)/(1 - ax) = (1 + a^2x)/(1 - ax)
Now we can cross-multiply to get rid of the denominator:
(1 + a^2x) = pq - axpq
Next, we can move the term with x to the left-hand side of the equation:
a^2x + axpq = pq - 1
Finally, we can factor out x from the two terms on the left-hand side:
x(a^2 + apq) = pq - 1
Therefore, we can isolate x by dividing both sides by (a^2 + apq):
x = (pq - 1)/(a^2 + apq)
So the correct option is: p-q / a(p+q) which is not among the given options.