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}

f (x) = \frac{- x}{x + 2}

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

\frac{x ^{2} + 4 x + 3}{x ^{2} + 6 x + 9}

arcsec (2 x)

f (x) = \frac{x + 1}{x ^{2} + 7 x + 6}

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