3p-2 p-3
__________ - _______
p^2+2p-24 P^2-16
Subtract and simplify
To subtract and simplify the expression
```
3p - 2 p - 3
__________________ - _________________
p^2 + 2p - 24 p^2 - 16
```
we need to find a common denominator for the two fractions. The denominators are `(p^2 + 2p - 24)` and `(p^2 - 16)`.
First, factorize the denominators:
```
p^2 + 2p - 24 = (p - 4)(p + 6)
p^2 - 16 = (p - 4)(p + 4)
```
So, the common denominator is `(p - 4)(p + 6)(p + 4)`.
Now let's rewrite the fractions with the common denominator:
```
(3p - 2)(p + 4) (p - 3)(p + 6)
________________ - _______________
(p - 4)(p + 6)(p + 4) (p - 4)(p + 6)(p + 4)
```
Next, expand the numerators:
```
3p^2 + 10p - 8 p^2 + 3p - 18
______________ - ______________
(p - 4)(p + 6)(p + 4) (p - 4)(p + 6)(p + 4)
```
Now, we can combine the fractions:
```
(3p^2 + 10p - 8 - p^2 - 3p + 18) / ((p - 4)(p + 6)(p + 4))
```
Simplifying the numerator:
```
2p^2 + 7p + 10
```
Therefore, the simplified expression is:
```
(2p^2 + 7p + 10) / ((p - 4)(p + 6)(p + 4))
```
And that is the final answer after subtracting and simplifying.