Subtract. State the difference in simplest form.
6/x-3 - 9/x+2
A. -3/x^2-x-6
B. -3x+39/x^2-x-6
C. -3x-1/x^2-x-6
D. -3x-15/x^2-x-6
To simplify the expression, we first need to find a common denominator for the two fractions:
6/x - 3 - 9/x + 2
= (6(x + 2) - 3(x - 3))/(x(x + 2))
Now, simplify the numerator:
= (6x + 12 - 3x + 9)/(x(x +2))
= (3x + 21)/(x(x + 2))
= 3(x + 7)/(x(x + 2))
Therefore, the answer is C. -3(x+7)/x(x+2)