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

The asymptotes of f(x)=(3x-1)/((2x+3)(2x-3)) is Vertical: x=-3/2 ,x= 3/2 ,Horizontal: y=0

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

asymptotes

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

Vertical : x = - \frac{3}{2}, x = \frac{3}{2}, Horizontal : y = 0

Solution steps

Vertical asymptotes of

\frac{3 x - 1}{( 2 x + 3 ) ( 2 x - 3 )} : x = - \frac{3}{2}, x = \frac{3}{2}

Horizontal Asymptotes of

\frac{3 x - 1}{( 2 x + 3 ) ( 2 x - 3 )} : y = 0

Slant Asymptotes of

\frac{3 x - 1}{( 2 x + 3 ) ( 2 x - 3 )} :

None

Vertical : x = - \frac{3}{2}, x = \frac{3}{2}, Horizontal : y = 0

(- 4, 2), (2, 4)

f (x) = \frac{x ^{2} + 1 + 8 x}{x ^{2} + 1 + 2 x}

f (x) = x^{2} - 2 x + 3

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

f (x) = - x^{2} + 8 x + 8

What is the asymptotes of f(x)=(3x-1)/((2x+3)(2x-3)) ?
The asymptotes of f(x)=(3x-1)/((2x+3)(2x-3)) is Vertical: x=-3/2 ,x= 3/2 ,Horizontal: y=0