SOLUTION: A problem that I have for homework is: "Write an example of a rational function that has asymptotes at x=4 and y=3" How do I find a correct example?

Question 156721: A problem that I have for homework is:
"Write an example of a rational function that has asymptotes at x=4 and y=3"
How do I find a correct example?
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
A function that has x and y asynptotes is
When approaches , x approaches infinity
and vice versa.
In order to move the asymptotes to and
, I change the equation to
or
plotting this:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The last solution was perfect, but you can simplify the equation:

Start with the given equation

Multiply the second term by

Combine the terms.

Distribute

Add the fractions.

Combine like terms.

So simplifies to
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