Evaluate the following Limitx-4 (x^2-4x)/(x^2-3x-4)?

Question

Evaluate the following Limitx-4 (x^2-4x)/(x^2-3x-4)?

Answer 1

yea you could factor: Limit x-4 x(x-4)/ (x+1)(x-4)=4/5

or use L'Hospital :Limit x-4 (4^2-4*4)/(4^2-3*4-4) = 0/0

=Limit x-4 d/dx(x^2-4x)/ d/dx(x^2-3x-4)

=Limit x-4 (2x-4)/ (2x-3) = 2*4-4 / 2*4-3 = 4/5

Answer 2

since both top and bottom are 0 at x = 4 means both have the factor [ x-4]...do the factoring and cancel, then take the limit