Simplifying a rational expression

How do you simplify this: (x^2 + 2x - 8) / (18 -7x -x^2)?

x^2 + 2x - 8
-------------
18 - 7x - x^2

x^2 + 2x - 8
-------------- {switched bottom around}
-x^2 - 7x + 18

x^2 + 2x - 8
---------------- {factored -1 out of bottom}
-1(x^2 + 7x - 18 )

(x + 4)(x - 2)
---------------- {factored top and bottom into two binomials}
-1(x + 9)(x - 2)

-(x + 4)
-------- {cancelled x - 2 on top and bottom}
(x + 9)

-x - 4
------- {distributed negative sign}
x + 9

© Algebra House