i've been asking for two hours, please help!!

Which of the following is an equation for the horizontal asymptote to the graph of y=3-(x+b/x-c) and how you get it?

Question

i've been asking for two hours, please help!!

Which of the following is an equation for the horizontal asymptote to the graph of y=3-(x+b/x-c) and how you get it?

anonymous · Answer

the one that has a vertical asymptote at $x=c$

anonymous · Answer

oh you want "horizontal asymptote" right ?

anonymous · Answer

the answer is y=2, but i dont know how to solve for it.

anonymous · Answer

yes

anonymous · Answer

method one 
add

anonymous · Answer

drawing will be helpful, thank you

anonymous · Answer

$$3-\frac{x+b}{x-c}$$
$$=\frac{3(x-c)-(x+b)}{x-c}$$
$$=\frac{2x+stuff }{x-c}$$

anonymous · Answer

you can find the stuff, but no matter since the numerator has leading coefficient 2 and the denominator has leading coefficient 1 so the horizontal asymptote is $y=2$

anonymous · Answer

what do you do after step 3

anonymous · Answer

method 2 (no algebra, just think)
$-\frac{x+b}{x-c}$ has horizontal asymptote $y=-1$ add $3$ and get $y=2$

anonymous · Answer

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