Find the limit: lim x->4 [(x+1)(x-4)]/[(x-1)(x-4)]

For x close to 4, but not equal to 4, the function reduces to (x+1)/(x-1),

which approaches (4+1)/(4-1) = 5/3

As you can see, the limit exists.

lim x->4 [(x+1)(x-4)]/[(x-1)(x-4)]= (x+1)/(x-1)=5/3