What is the asymptotes of f(x)=(2x^2-x+6)/(3x+5) ?

The asymptotes of f(x)=(2x^2-x+6)/(3x+5) is Vertical: x=-5/3 ,Slant: y= 2/3 x-13/9

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asymptotes of f(x)=(2x^2-x+6)/(3x+5)

asymptotes

f (x) = \frac{2 x ^{2} - x + 6}{3 x + 5}

Vertical : x = - \frac{5}{3}, Slant : y = \frac{2}{3} x - \frac{13}{9}

Solution steps

Vertical asymptotes of

\frac{2 x ^{2} - x + 6}{3 x + 5} : x = - \frac{5}{3}

Horizontal Asymptotes of

\frac{2 x ^{2} - x + 6}{3 x + 5} :

None

Slant Asymptotes of

\frac{2 x ^{2} - x + 6}{3 x + 5} : y = \frac{2}{3} x - \frac{13}{9}

Vertical : x = - \frac{5}{3}, Slant : y = \frac{2}{3} x - \frac{13}{9}

f (x) = \frac{4 x ^{2} - 16}{- 3 x ^{2} + 6 x}

\frac{x + 2}{x ^{2} + 2 x - 3}

f (x) = \frac{1}{x} + x

\frac{x ^{2} - 3 x - 4}{x ^{2} - 16}

f (x) = \frac{x ^{2} - 1}{x ^{2} - x - 2}

What is the asymptotes of f(x)=(2x^2-x+6)/(3x+5) ?
The asymptotes of f(x)=(2x^2-x+6)/(3x+5) is Vertical: x=-5/3 ,Slant: y= 2/3 x-13/9