SOLUTION: For the function: f(x)= x-3/(-2x+3)(2x+7),what is the vertical asymptote s? Give a list of x-value separated by a comma. What is the horizontal asymptote?

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Question 611744: For the function: f(x)= x-3/(-2x+3)(2x+7),what is the vertical asymptote s? Give a list of x-value separated by a comma. What is the horizontal asymptote?
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
The vertical asymptotes, if any, occur for x values that make a denominator zero. So to find the vertical asymptotes for your function, you just set the denominator equal to zero and solve for x:
(-2x+3)(2x+7) = 0

With one side zero and the other side already factored, this is easy to solve. From the Zero Product Property we know that one of the factors must be zero. So:
-2x+3 = 0 or 2x+7 =0
Solving these we get:
or
These are the x values where there will be vertical asymptotes.

For the horizontal asymptotes:
There will be no horizontal asymptotes if the degree of the numerator is greater than the degree of the denominator.
The horizontal asymptote will be y = 0 if the degree of the numerator is less than the degree of the denominator.
If the degrees of the numerator and denominator are equal, then the horizontal asymptote will be the ratio of the leading coefficient of the numerator over the leading coefficient of the denominator.

The degree of your numerator is 1 (since the highest power of x is 1) and the degree of your denominator is 2 (since there would be an term if you multiplied it out). So your function fits the middle case above. The horizontal asymptote is y = 0.

P.S. I re-categorized your problem. Picking the right category for your posts will increase the speed of a response.