What is the asymptotes of f(x)=(x^2+3x+1)/(4x^2-9) ?

The asymptotes of f(x)=(x^2+3x+1)/(4x^2-9) is Vertical: x=-3/2 ,x= 3/2 ,Horizontal: y= 1/4

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asymptotes of f(x)=(x^2+3x+1)/(4x^2-9)

asymptotes

f (x) = \frac{x ^{2} + 3 x + 1}{4 x ^{2} - 9}

Vertical : x = - \frac{3}{2}, x = \frac{3}{2}, Horizontal : y = \frac{1}{4}

Solution steps

Vertical asymptotes of

\frac{x ^{2} + 3 x + 1}{4 x ^{2} - 9} : x = - \frac{3}{2}, x = \frac{3}{2}

Horizontal Asymptotes of

\frac{x ^{2} + 3 x + 1}{4 x ^{2} - 9} : y = \frac{1}{4}

Slant Asymptotes of

\frac{x ^{2} + 3 x + 1}{4 x ^{2} - 9} :

None

Vertical : x = - \frac{3}{2}, x = \frac{3}{2}, Horizontal : y = \frac{1}{4}

2 x + 5 y - 8 = 0

x^{4} - x^{2} + 3

y = 3 x - 4

x - \frac{1}{x}

m = \frac{2}{3}

What is the asymptotes of f(x)=(x^2+3x+1)/(4x^2-9) ?
The asymptotes of f(x)=(x^2+3x+1)/(4x^2-9) is Vertical: x=-3/2 ,x= 3/2 ,Horizontal: y= 1/4