Answer:
vertical asymptote: x = 3
slant asymptote: y = x+5
Explanation:
You want the vertical and slant asymptote of the graph of the rational function ...
y = (x² +2x -3)/(x -3)
Quotient
Using synthetic division (see the first attachment), we find the quotient to be (x+5) and the remaining rational function term to be 12/(x-3).
Vertical asymptote
There is a vertical asymptote at the value of x where the denominator is zero: x = 3.
Slant asymptote
The slant asymptote is the polynomial part of the quotient:
y = x +5
The asymptotes are the orange dashed lines in the second attachment.
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