If  $\frac{2}{x-3}$ - $\frac{3}{x-2}$ = $\frac{p}{(x-3)(x -2)}$, find p.

Step 1: Analyze the question We need to combine the two fractions on the left into a single fraction and compare the numerator with p.

Step 2: Concept To subtract fractions, use the common denominator (x − 3)(x − 2).

Step 3: Solution

Expand the numerator:

• 2(x − 2) = 2x − 4
• 3(x − 3) = 3x − 9

Subtract:

2x − 4 − (3x − 9) = 2x − 4 − 3x + 9 = −x + 5 = 5 − x

So

Comparing with the right-hand side, p = 5 − x.

Step 4: Answer The correct option is A. 5 − x.

Tip: When subtracting fractions, put brackets around the second numerator after multiplying, such as −(3x − 9). The most common mistake is forgetting to change the sign of the +9. Note that the options include −(x + 5), which comes from that kind of sign error.