# Graph y=x+1/x

Find where the expression is undefined.

Consider the rational function where is the degree of the numerator and is the degree of the denominator.

1. If , then the x-axis, , is the horizontal asymptote.

2. If , then the horizontal asymptote is the line .

3. If , then there is no horizontal asymptote (there is an oblique asymptote).

Find and .

Since , there is no horizontal asymptote.

No Horizontal Asymptotes

Find the oblique asymptote using polynomial division.

Click for detailed explanation...

Combine.

Click for detailed explanation...

To write as a fraction with a common denominator, multiply by .

Combine the numerators over the common denominator.

Multiply by .

Simplify.

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .

+ | + | + |

Divide the highest order term in the dividend by the highest order term in divisor .

+ | + | + |

Multiply the new quotient term by the divisor.

+ | + | + | |||||||

+ | + |

The expression needs to be subtracted from the dividend, so change all the signs in

+ | + | + | |||||||

- | - |

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

+ | + | + | |||||||

- | - | ||||||||

Pull the next term from the original dividend down into the current dividend.

+ | + | + | |||||||

- | - | ||||||||

+ |

The final answer is the quotient plus the remainder over the divisor.

The oblique asymptote is the polynomial portion of the long division result.

This is the set of all asymptotes.

Vertical Asymptotes:

No Horizontal Asymptotes

Oblique Asymptotes:

- Evaluate find the value of cube root of 64
- Solve for x log base 6 of 2x+3=3
- Graph 6x-3y=9
- Solve by Factoring cube root of 20x=-4
- Simplify square root of 25x^16
- Simplify 5 square root of 2*9 square root of 6
- Evaluate 3.100
- Solve for u 13/8=u/9
- Find the Area Between the Curves y=x , y = fourth root of x
- Solve for x sin(x)^2+3cos(x)^2=0