Subtract. State the difference in simplest form.
6/x-3 - 9/x+2
To subtract these two expressions, we need to have a common denominator. The common denominator for x-3 and x+2 is (x-3)(x+2).
So, our expression becomes:
(6(x+2) - 9(x-3)) / ((x-3)(x+2))
Expanding the numerator:
(6x + 12 - 9x + 27) / ((x-3)(x+2))
(-3x + 39) / ((x-3)(x+2))
Therefore, the difference in simplest form is (-3x + 39) / ((x-3)(x+2)).