Question

Find the quotient and any excluded values.

(x + 5/x^2 + 9x + 20)/(x^2-16/x-4)

Answer 1

By (x + 5/x^2 + 9x + 20) you apparently meant the following:

x+5
----------------------
x^2 + 9x + 20

and by

(x^2-16/x-4)
x^2-16
you apparently meant ---------------
x - 4

Please use additional parentheses for clarity.

Dividing,

x+5 (x-4)(x+4)
---------------------- * ---------------
x^2 + 9x + 20 x-4

Now, x^2 + 9x + 20 factors into (x+4)(x+5), so what we have now is

(x+5)(x+4)
------------------------- = 1 This is true for all x, so there are no exclusions.
(x+4)(x+5)