simplify into one fraction 3/x-3 - 5/x-2

Answer 1

To simplify the expression (3/x-3) - (5/x-2), we first need to find a common denominator for the fractions. The least common denominator for x -3 and x -2 is (x -3)(x -2), which is the same as (x-3)(x-2).

Now, we rewrite the fractions with the common denominator:

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

Combining the fractions by subtracting them:

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

Now, combine like terms in the numerator:

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

Therefore, the simplified expression is (-2x + 9)/((x-3)(x-2))