Find coordinates of symmetry of y = ((x+a)(x-1)) / (x-a)

[baked]

Hi Everyone!
How do I find the coordinates of symmetry of the graph of:
[math]\frac{(x+a)(x-1)}{x-a}\\[/math]
I've started by dividing the numerator by the denominator, perhaps getting an oblique asymptote?

I resulted in the answer of: [math]x+(2a-1) + \frac{-2a-2a^2}{x-a}\\[/math]I don't think this is correct... so any help would really be appreciated. Thank you!!

 

[Dr.Peterson]

How do I find the coordinates of symmetry of the graph of:
[math]\frac{(x+a)(x-1)}{x-a}\\[/math]
I've started by dividing the numerator by the denominator, perhaps getting an oblique asymptote?

I resulted in the answer of: [math]x+(2a-1) + \frac{-2a-2a^2}{x-a}\\[/math]I don't think this is correct... so any help would really be appreciated. Thank you!!

No, that is correct as far as I can see, except perhaps one minor sign error in the division.

But I don't know what "coordinates of symmetry" are! You will have an oblique asymptote, and a vertical asymptote, each of which you just need to state based on what you've shown; what else do you want to find?

One observation is that the behavior of the function will depend on the value of a; it should be easy to see that a=1 and a=0 will be special cases, and there will be (at least) 3 separate cases to consider for the intervals separated by those values.