PLEASE HELP WILL MARK BRAINIEST Create a rational expression that satisfies the following criteria:
1) Domain is all reals except 1 and -1
2) x=1 is a vertical asymptote
3) X = -1 is a hole
4) There is a horizontal asymptote at y = 3

y = (3x² + x - 2)/(x² - 1)

Step-by-step explanation:

(x - 1)(x + 1) = x² - 1

In the denominator

f(x)/(x² - 1)

f(x) has a factor (x + 1)

3 + (x + 1)/(x² - 1)

(3x² - 3 + x + 1)/(x² - 1)

y = (3x² + x - 2)/(x² - 1)

Step-by-step explanation:

Vertical asymptotes are places where the denominator of a rational expression equals 0 because in those scenarios, we have something like k/0, where k is any expression. This is undefined.

Since x = 1 is a vertical asymptote, we need to make sure we put (x - 1) in the denominator because when we set that equal to 0, we get x = 1.

The domain says that it's all reals except 1 and -1. Domain is all the possible x values. We already covered 1 because we put (x - 1) in the denominator. Similarly, to make sure that the domain doesn't include -1, we need to put x + 1 in the denominator.

Now, we see that x = -1 is a hole. A hole is a removable point of discontinuity. This means that (x + 1) needs to be in the denominator and numerator. That way, we can "remove" it by cancelling it out from the top and bottom, but it still counts as a vertical asymptote.

Finally, there is a horizontal asymptote at y = 3. We get horizontal asymptotes when y approaches a value. A property of horizontal asymptotes is that when the degree of the numerator and denominator of a rational expression are equal, the horizontal asymptote is just the ratio of their leading coefficients. That's why I made sure that both the top and bottom had degrees of 2 by adding an x to the numerator, and I also added a 3 to the numerator so that the leading coefficient of the numerator is 3 and leading coefficient of the denominator is 1, making the ratio 3:1 = 3.

Hope this helps!

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.