Question

Rational expressions help.. ???

Answer 1

\[\frac{ 9 }{ x } - \frac{ 1 }{ x }\]

Answer 2

Simplify and list any discontinuities and identify the type of discontinuity.

Answer 3

@ikram002p @imqwerty

Answer 4

I'm gueesing its 8/x.... im confused on the discontinuity part.

Answer 5

oh god, i hated these. dnt worry i got you love!

Answer 6

when adding or subtracting fractions you need the same denominators
in this case, both have the same bottom, an x
so you can write
\[ \frac{9}{x}-\frac{1}{x}= \frac{9-1}{x} \\= \frac{8}{x} \]

of course, you are not allowed to divide by zero, so we say: \( x\ne 0\)
(i.e. x is not allowed to be 0)

Answer 7

@phi How do i find the discontinuities ?

Answer 8

@phi

Answer 9

the discontinuities happen because we don't allow divide by zero

Answer 10

is it vertical asymptote ? horizontal asymptote? or oblique asymptote ?

Answer 11

if you had, for example,
\[ \frac{x}{x+1} \]
you would try to find what x values make x+1 be zero
(you might notice x=-1 would cause -1+1 to be 0)
or you would write
x+1=0
and "solve for x" (add -1 to both sides)
you would get
x+1-1= 0-1 or
x=-1

there is a discontinuity at x=-1

Answer 12

if you have 8/x

at x= 0.1 (near 0 but not zero) you would get 8/0.1 = 80
at x=0.01 you would get 8/0.01 = 800
as you get x very close to 0 (e.g. 0.0000001)
8 divided by x gets really big.
if you plot these numbers, as you get near 0, the plot zooms straight up

Answer 13

so its vertical ?

Answer 14

yes