Explain why ModifyingBelow lim With x right arrow 6 StartFraction x squared minus 4 x minus 12 Over x minus 6 EndFractionlimx→6 x2−4x−12x−6equals=ModifyingBelow lim With x right arrow 6 left parenthesis x plus 2 right parenthesislimx→6 (x+2).

Choose the correct answer below.

A.

Since each limit approaches

66,

it follows that the limits are equal.

B.

Since

StartFraction x squared minus 4 x minus 12 Over x minus 6 EndFraction equals x plus 2x2−4x−12x−6=x+2

whenever

xnot equals≠66,

it follows that the two expressions evaluate to the same number as x approaches

66.

C.

The numerator of the expression

StartFraction x squared minus 4 x minus 12 Over x minus 6 EndFractionx2−4x−12x−6

simplifies to

x plus 2x+2

for all x, so the limits are equal.

D.

The limits

ModifyingBelow lim With x right arrow 6 StartFraction x squared minus 4 x minus 12 Over x minus 6 EndFractionlimx→6 x2−4x−12x−6

and

ModifyingBelow lim With x right arrow 6 left parenthesis x plus 2 right parenthesislimx→6 (x+2)

equal the same number when evaluated using direct substitution.