(x^(2)-6x-27)/(x^(2)-6x+9)-(x^(2)-x-20)/(x^(2)+10x+24)

Answer 1

To simplify the given expression, we first factor the denominators of each fraction:

x^2 - 6x - 27 factors to (x-9)(x+3)
x^2 - 6x + 9 factors to (x-3)(x-3)
x^2 - x - 20 factors to (x-5)(x+4)
x^2 + 10x + 24 factors to (x+6)(x+4)

Now, the expression becomes:

[(x-9)(x+3)/(x-3)(x-3)] - [(x-5)(x+4)/(x+6)(x+4)]

Now, we simplify each fraction:

(x-9)(x+3)/(x-3)(x-3) = (x-9)/(x-3)
(x-5)(x+4)/(x+6)(x+4) = (x-5)/(x+6)

Therefore, the final simplified expression is:

(x-9)/(x-3) - (x-5)/(x+6)