Help! The slant asymptote of #f(x)=(6x^3-5x^2+3x)/(3x^2-x-14)# intersects f where x=?

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Answer 1 · 2018-05-19T18:10:57

#y=2x-1#

x-int: #x= 1/2#

Use polynomial division to divide the numerator by the denominator the result is the line that is your slant asymptote.

#(6 x^3 - 5 x^2 + 3 x)/(3 x^2 - x - 14)#

#6 x^3 - 5 x^2 + 3 x = (2 x - 1) × (3 x^2 - x - 14) + 30 x - 14#

so the line #y=2x-1# is your slant asymptote

the x-int is where #y=0#:

#0=2x-1#

#x= 1/2#