$\"\"$

The function is $\"f\\left$ .

$\"P(x)\"$ is a polynomial function.

The function $\"f(x)\"$ has a vertical asymptote at $\"x=1\"$ .

If $\"P(x)\"$ is divisible by $\"x-1\"$ , then the function $\"f(x)\"$ has removable discontinuity at $\"x=1\"$ .

If $\"P(x)\"$ is not divisible by $\"x-1\"$ , then the function $\"f(x)\"$ has discontinuity at $\"x=1\"$ .

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$\"f(x)\"$ will have a vertical asymptote at $\"x=1\"$ if and only if $\"P(x)\"$ is not divisible by $\"x-1\"$ .