Question

@phi

Answer 1

\[\frac{ x^2 }{ (x+4) } - \frac{ 16 }{ (x+4) }\]

Answer 2

simplify and find discontinuities.

Answer 3

you have two fractions, with the same bottoms
so what do you do ?

Answer 4

if you factor the top, you get (x - 4) (x + 4) right ?

Answer 5

combine the like terms in numerator

Answer 6

yes
you get
\[ \frac{(x-4)(x+4)}{x-4}\]
you can "cancel" the (x-4) / (x-4)
as long as x is not 4 (other wise it is 0/0 and that is not allowed)

Answer 7

u mean cancel the (x + 4) right ?

Answer 8

and discontinuity ?

Answer 9

oops, it's
\[ \frac{(x-4)(x+4)}{(x+4)} \]
yes you cancel the (x+4)

but only if you don't allow x to be -4

Answer 10

ok... and the discontinuities ?

Answer 11

vertical horizontal or oblique ?

Answer 12

discontinuity is a name for the x value we don't allow.

because (x+4)/(x+4) is 1 it cancels
except if x is -4, because then it becomes 0/0 and that is not 1 (it is not defined)

so the discontinuity is at x=-4

Answer 13

and what type is it ?

Answer 14

just like before, as x gets close to -4, the number in the bottom gets tiny , and the fraction becomes huge. We get "zooming" up

Answer 15

so vertical.. ok