Which statement is true about the discontinuities of the function f(x)?

f(x)=x^2-4/x^3-x^2-2x

a. There is a hole x=2
b. There are asymptotes at x=0 and x=-1
c. There are asymptotes at x=0 and x=-1 and a hole at (2,2/3)
d. There are holes at x=-0 and x=-1 and an asymptote at x=-2

the correct answer is a.) bc< mn 5 stars if this you : )

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)