Question 77445
=(6x-24+3x^2)/(5-26x+ 5x^2)

=(3^2+6x-24)/(5x^2-26x+5)

=3(x^2+2x-12)/(5x^2-25x-x+5)

=3(x^2+2x-12)/(5x(x-5)-(x-5))

=3(x^2+2x-12)/(x-5)(5x-1)
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This site will not support graphing your rational function.
Vertical asymptotes at x=5 and at x=1/5
Horizontal asymptote at y=3/5
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Cheers,
Stan H.