limit as x approaches infinity of (5x^2-8x-13)/(x^2-5)

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lim_{x→ ∞}(5x²−8x−13x²−5 )

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lim_{x→ ∞}(5x²−8x−13x²−5 )

Divide by highest denominator power: 5−8x −13x² 1−5x²

=lim_{x→ ∞}(5−8x −13x² 1−5x² )

lim_x→a[f(x)g(x) ]=lim_x→af(x)lim_x→ag(x) , lim_x→ag(x)≠0
With the exception of indeterminate form

=lim_{x→ ∞}(5−8x −13x² )lim_{x→ ∞}(1−5x² )

lim_{x→ ∞}(5−8x −13x² )=5

lim_{x→ ∞}(1−5x² )=1

=51

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