Question

[15 Points]

Find the quotient with the restrictions.

(x^2 - 2x - 3) (x^2 + 4x + 3)
----------------- ÷ ------------------
(x^2 + 2x - 8) (x^2 + 6x + 8)

Answer 1

(x^2 - 2·x - 3)/(x^2 + 2·x - 8) + (x^2 + 4·x + 3)/(x^2 + 6·x + 8)

= ((x + 1)·(x - 3))/((x - 2)·(x + 4)) + ((x + 1)·(x + 3))/((x + 2)·(x + 4))

= ((x + 1)·(x - 3)·(x + 2))/((x + 2)·(x - 2)·(x + 4)) + ((x + 1)·(x + 3)·(x - 2))/((x + 2)·(x - 2)·(x + 4))

= ((x + 1)·(x - 3)·(x + 2) + (x + 1)·(x + 3)·(x - 2))/((x + 2)·(x - 2)·(x + 4))

= (x + 1)·((x - 3)·(x + 2) + (x + 3)·(x - 2))/((x + 2)·(x - 2)·(x + 4))

= (x + 1)·(x^2 - x - 6 + x^2 + x - 6)/((x + 2)·(x - 2)·(x + 4))

= (x + 1)·(2·x^2 - 12)/((x + 2)·(x - 2)·(x + 4))

= 2·(x + 1)·(x^2 - 6)/((x + 2)·(x - 2)·(x + 4))