3/x-3 - 5/x-2

Answer 1

To simplify this expression, we need to find a common denominator for both fractions:

3/(x-3) - 5/(x-2)

The common denominator for (x-3) and (x-2) is (x-3)(x-2), which means we need to multiply the numerator and denominator of the first fraction by (x-2) and the numerator and denominator of the second fraction by (x-3):

(3(x-2))/(x-3)(x-2) - (5(x-3))/(x-3)(x-2)

Now, we can combine the fractions:

(3x-6-5x+15)/(x-3)(x-2)

(-2x+9)/(x-3)(x-2)

Therefore, 3/x-3 - 5/x-2 simplifies to (-2x+9)/(x-3)(x-2).