find asymptotes 2 help

[bcddd214]

f(x)=(2x^5+x^3-1)/(-6x^4+5)

once again, I look at the denominator and think (complete the square and be done with it).
This route did me no help/luck

 

[tkhunny]

Factor the denominator. Use all Real numbers. Don't stop at integers.

 

[bcddd214]

Factor the denominator. Use all Real numbers. Don't stop at integers.

Finally an answer. Now I am tired.
Good night
Maybe I will be back.....

 

[masters]

Factor the denominator. Use all Real numbers. Don't stop at integers.

Finally an answer. Now I am tired.
Good night
Maybe I will be back.....

A simple "Thank you" might be in order.

 

[soroban]

Hello, bcddd214!

Did you find all the answers?

\(\displaystyle \text{Find the asympototes: } f(x)\:=\:\frac{2x^5+x^3-1}{-6x^4+5}\)

Vertical asymptotes occur where the denominator equals zero.

. . \(\displaystyle -6x^4 + 5 \:=\:0 \quad\Rightarrow\quad x^4 \:=\:\tfrac{5}{6}\)

\(\displaystyle \text{Vertical asymptotes: }\:x \:=\:\pm\sqrt[4]{\tfrac{5}{6}}\)


\(\displaystyle \text{Long division: }\:f(x) \:=\:-\tfrac{1}{3}x - \frac{3x^5 + 5x - 3}{3(6x^4 - 5)}\)

\(\displaystyle \text{Oblique asymptote: }\:y \:=\:-\tfrac{1}{3}x\)