Simplify expression, write final answer without negative exponents.

(x-3/x-4)- (x+2/x+1) all over (x+3)

is the answer: (-8x+5) / x+3 ?

please help!

To simplify the given expression and write the final answer without negative exponents, we need to follow these steps:

Step 1: Simplify each fraction individually.
(x-3)/(x-4) can be left as is since there are no negative exponents in the numerator or denominator.
Similarly, (x+2)/(x+1) can also be left as is.

Step 2: Combine the fractions by finding a common denominator.
The common denominator for both fractions is (x-4)(x+1).

(x-3)/(x-4) = [(x-3)(x+1)] / [(x-4)(x+1)]
(x+2)/(x+1) = [(x+2)(x-4)] / [(x-4)(x+1)]

Step 3: Subtract the fractions.
[(x-3)(x+1)] / [(x-4)(x+1)] - [(x+2)(x-4)] / [(x-4)(x+1)]

Step 4: Simplify the expression by expanding and canceling out terms.
[(x^2 - 3x + x - 3)] / [(x-4)(x+1)] - [(x^2 - 2x - 4x + 8)] / [(x-4)(x+1)]
[(x^2 - 2x - 3)] / [(x-4)(x+1)] - [(x^2 - 6x + 8)] / [(x-4)(x+1)]

Next, perform the subtraction by combining the terms in the numerator:
[(x^2 - 2x - 3) - (x^2 - 6x + 8)] / [(x-4)(x+1)]
[(x^2 - 2x - 3 - x^2 + 6x - 8)] / [(x-4)(x+1)]
[(4x - 11)] / [(x-4)(x+1)]

Finally, we can write the simplified expression without negative exponents as:
(4x - 11) / ((x-4)(x+1))

Therefore, the final answer is (4x - 11) / (x^2 - 3x - 4).