# f(x)=(x2−2ax)/(x−a) where a is positive. The question asks to give equations for the 2 asymptotes. The first is obvious: x=a. The other asymptote is y=x−a but I am unsure how to derive this.

Asymptotes for a function
$f\left(x\right)=\frac{{x}^{2}-2ax}{x-a}$
where a is positive.
The question asks to give equations for the 2 asymptotes. The first is obvious: x=a. The other asymptote is y=x−a but I am unsure how to derive this.
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Dominic Paul
Rewrite the function:
$f\left(x\right)=\frac{{x}^{2}-2ax}{x-a}=\frac{{x}^{2}-2ax+{a}^{2}-{a}^{2}}{x-a}=\frac{\left(x-a{\right)}^{2}-{a}^{2}}{x-a}=x-a-\frac{{a}^{2}}{x-a}$
Now both the stated asymptotes are obvious: a vertical one (x=a) and an oblique one (y=x−a).