What is the asymptotes of f(x)=(3x^2-27)/(2x^2+5x-3) ?

The asymptotes of f(x)=(3x^2-27)/(2x^2+5x-3) is Vertical: x= 1/2 ,Horizontal: y= 3/2

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asymptotes of f(x)=(3x^2-27)/(2x^2+5x-3)

asymptotes

f (x) = \frac{3 x ^{2} - 27}{2 x ^{2} + 5 x - 3}

Vertical : x = \frac{1}{2}, Horizontal : y = \frac{3}{2}

Solution steps

Vertical asymptotes of

\frac{3 x ^{2} - 27}{2 x ^{2} + 5 x - 3} : x = \frac{1}{2}

Horizontal Asymptotes of

\frac{3 x ^{2} - 27}{2 x ^{2} + 5 x - 3} : y = \frac{3}{2}

Slant Asymptotes of

\frac{3 x ^{2} - 27}{2 x ^{2} + 5 x - 3} :

None

Vertical : x = \frac{1}{2}, Horizontal : y = \frac{3}{2}

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

f (x) = \frac{3 x ^{3}}{4 x ^{2} - 8 x}

\frac{1}{\frac{20}{x - 5} - 2}

\frac{x ^{2} + 1}{x - 2}

\frac{x - 5}{2 x + 7}

What is the asymptotes of f(x)=(3x^2-27)/(2x^2+5x-3) ?
The asymptotes of f(x)=(3x^2-27)/(2x^2+5x-3) is Vertical: x= 1/2 ,Horizontal: y= 3/2