How do you simplify (x^2 + 5x + 4 )/ (x^2 - 16)?

1 Answer
Mar 9, 2018

(x+1)/(x-4)," ""if "x+4!= 0

Explanation:

Step 1: Factor both the numerator and denominator.

(x^2 + 5x + 4)/(x^2 - 16) = [(x+1)(x+4)]/[(x-4)(x+4)]

Step 2: Cancel common factors.

[(x+1)cancel((x+4))]/[(x-4)cancel((x+4))]= (x+1)/(x-4)," ""if "x+4!= 0

Why write this "if x+4!=0" part? Because in the original quotient, if x+4=0 (that is, if x=–4), then the denominator would equal zero, and division by zero is undefined.

On its own, (x+1)/(x-4) does not give the same problem when x=–4. Since we want our simplified expression to reflect the original one in its entirety, we make sure it has all the same restrictions, including x+4!=0.