How do you use long division find the oblique asymptote #h(x) = 10x^3/(2x^2 -1)#?

1 Answer
Rafael
Oct 7, 2015

#y=5x#

Explanation:

To find the oblique asymptote of this rational function, simply divide #10x^3# by #2x^2-1#, then take the polynomial part (not including the remainder).

Solution:
#color(white)(xxxxxx)ul((5x)(Polynomial Part))#
#2x^2-1|##color(white)(x)10x^3#
#color(white)(xxxxx)-10x^3+5x#
#color(white)(xxxxxxxxxxxx)5x(Remai##nder)#

The polynomial part is 5x, so the equation of the oblique asymptote is #y=5x#.

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