Perform the indicated operation 3x over X-5 minus 2x over X-2

Solution:
1. Given expressions:

- \frac{3x}{x-5}
- \frac{2x}{x-2}

2. Find the common denominator.
- The denominators are (x-5) and (x-2).
- The common denominator is (x-5)(x-2).

3. Rewrite each fraction with the common denominator:
- \frac{3x}{x-5} = \frac{3x(x-2)}{(x-5)(x-2)} = \frac{3x^2 - 6x}{(x-5)(x-2)}
- \frac{2x}{x-2} = \frac{2x(x-5)}{(x-5)(x-2)} = \frac{2x^2 - 10x}{(x-5)(x-2)}

4. Subtract the fractions:
\frac{3x^2 - 6x}{(x-5)(x-2)} - \frac{2x^2 - 10x}{(x-5)(x-2)} = \frac{(3x^2 - 6x) - (2x^2 - 10x)}{(x-5)(x-2)}

5. Simplify the numerator:
3x^2 - 6x - (2x^2 - 10x) = 3x^2 - 6x - 2x^2 + 10x = x^2 + 4x

6. Final expression:
\frac{x^2 + 4x}{(x-5)(x-2)}