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How many vertical asymptotes does the equation $y=\frac{x-1}{x^2+6x-7}$ have?

 Aug 4, 2020
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To determine vertical asymptotes, you must first factor both the numerator and denominator and cancel

out those factors which are found in both the numerator and denominator.

 

y  =  (x - 1) / (x2 + 6x - 7)  =  (x - 1) / [ (x - 1)·(x + 7) ]  =  1 / (x + 7)

 

Because there is a factor of (x + 7) remaining in the denominator, there is one vertical asymptote,

at x = -7.

 

The factor (x - 1) does not give a vertical asymptote, instead, it creates a "hole" in the graph at x = 1.

 Aug 4, 2020

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