How do you find vertical, horizontal and oblique asymptotes for $(x^2-9x+4)/(x+6)$ ?

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Answer 1 · 2016-05-31T12:38:09

The vertical asymptote as at $" "x=-6$
The oblique asymptote is $" "y=x-15$

Given: $" "(x^2-9x+4)/(x+6)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Determine the vertical asymptote")$

The equation is undefined at the denominator being 0

So the excluded value is that which gives $1+6= 0$

$color(green)("So the vertical asymptote as at "x=-6)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(blue)("Determine the oblique asymptote")$

Investigate the extreme values of $x$

$color(brown)("I can not spot how to simplify the given expression so by")$
$color(brown)("polynomial division we have "y= x-15+94/(x+6))$

$y=lim_(x->color(white)()^(-)oo ) x-15+94/(x+6)" "=" "x-15$

$color(green)("So the oblique asymptote is "y=x-15)$

Tony B

How do you find vertical, horizontal and oblique asymptotes for (x^2-9x+4)/(x+6)(x^2-9x+4)/(x+6)?