Fractions in all honesty are quite simply a pain. They complicate things greatly. Luckily we can cancel out some of the fractions here. Note we have inner fractions 3/(x-2) and 4/(x-2), both of which having a denominator of (x-2).
Focus on just the stuff up top which is 3/(x-2) - 5. Multiply both of the terms by the expression (x-2) to get the fraction 3/(x-2) turning into just 3. The 5 becomes 5(x-2) = 5x-10. So we end up with the expression 3 - (5x-10) = 3-5x+10 = 13-15x up top
Similarly, in the denominator we have 2 - (4/(x-2)) which becomes 2(x-2) - 4 = 2x-4-4 = 2x-8 when we multiply everything by (x-2) to cancel out that inner fraction.
So that's how we end up with (13-5x) all over (2x-8) as our final answer.
