The function has a vertical asymtote at and .

The function has a oblique asymtote at .

Vertical Asymptotes :

The rational function has vertical asymptotes at and , therefore the zeros of the denominator should not be and .

Therefore the factors of the denominator are and .

Oblique Asymptote :

Since there is an oblique asymptote , the degree of the numerator is exactly  greater than the degree of the denominator.

Additionally, when the numerator is divided by the denominator, the quotient polynomial is .

The function can be written as , where is numerator of the function.

, where is remainder of the function.

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The denominator of can be written as ,which is used to solve the equation .

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Multiply each side by .

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The degree of the remainder has to be less than the degree of the denominator, so it will either be  or .

Thus, the sum of cannot be determined, but the first two terms of  must be .

Substitute this expression for and use long division to verify that the quotient is .

Long Division Method :

The dividend is .

The divisor is .

Rewrite the expression in long division form .

Divide the first term of the dividend by the first term of the divisor .

So, the first term of the quotient is .

Multiply by and subtract.

The remainder is the last entry in the last row.

Therefore, the remainder .

The quotient is .

Thus the function is .

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