Find vertical asymptote. f(x) = x^2/2x^2-x-3

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`f(x) = x^2/(2x^2-x-3)`

`f(x) = x^2/(2x^2-3x+2x-3)`

`f(x) = x^2/(2x(x+1)-3(x+1))`

`f(x) = x^2/((x+1)(2x-3))`

 

The definition of a vertical asymptote

The line x = a is a vertical asymptote of `y = f(x)` if it will satisfy one of the following conditions.

`lim_(xrarr(oo)^-)f(x) = +-oo`

`lim_(xrarr(oo)^+)f(x) = +-oo`

 

`f(x) = x^2/((x+1)(2x-3))`

 

`lim_(xrarra)x^2/((x+1)(2x-3)) = +-oo` when `(x+1)(2x-3) = 0`

`(x+1)(2x-3) = 0`

`x = -1` or `x = 3/2`

 

So the vertical asymptotes are x = -1 and x = 3/2

 

 

 

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