3/2x+3 - 5/x-7 + x^2-x/2x^2-11x-21

To simplify the given expression, we need to combine like terms and then factor wherever possible. Let's follow these steps:

Step 1: Find a common denominator for all the fractions.
The denominators in the expression are (2x + 3), (x - 7), and (2x^2 - 11x - 21). To find a common denominator, we need to factor the last denominator.

Factoring (2x^2 - 11x - 21):
We can find two numbers that multiply to give -42 (-21 * 2) and add up to -11. These numbers are -14 and +3.
So, we can rewrite 2x^2 - 11x - 21 as 2x^2 - 14x + 3x - 21.

Now, we group the terms: (2x^2 - 14x) + (3x - 21).

Factoring out common factors, we have:
2x(x - 7) + 3(x - 7).

The factored form is (2x + 3)(x - 7).

Step 2: Rewrite the expression with the common denominator.
Using the factored form of the third denominator, the expression becomes:
3/(2x + 3) - 5/(x - 7) + (x^2 - x)/(2x + 3)(x - 7).

Step 3: Find the least common denominator.
The least common denominator is simply the product of all the denominators, so it is (2x + 3)(x - 7).

Step 4: Rewrite the fractions with the least common denominator.
Multiply the numerator and denominator of each fraction by the missing factors to get the common denominator:
3(x - 7)(x - 7)/(2x + 3)(x - 7) - 5(2x + 3)/(2x + 3)(x - 7) + (x^2 - x)/(2x + 3)(x - 7).

Simplify each fraction separately:
(3x^2 - 42x + 147 - 10x - 15 + x^2 - x)/(2x + 3)(x - 7).

Combine like terms in the numerator:
(4x^2 - 52x + 132)/(2x + 3)(x - 7).

Finally, the simplified form of the expression is:
(4x^2 - 52x + 132)/(2x + 3)(x - 7).