I've got this problem: (x^2+10x+16)/(x+2) how do you do it?

Question

(x^2+10x+16) / (x+2)

Answer 1

Factorise the numerator: (x+2)(x+8). The denominator divides into this leaving x+8.

However, the division is only valid if x+2 is non-zero, i.e., x not equal to -2, because that would cause division by zero, which is not permitted. When x is very close to -2 the result of the division is still x+8, so we could state that the limit as x approaches -2 is nevertheless x+8=6 when x=-2.