# How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x) = (2x-2) / ((x-1)(x^2 + x -1))#?

##### 1 Answer

Horizontal:

Vertical:

#### Explanation:

If y = f(x)/g(x) and both f and g have the same factor h(x), then

y= (f(x)/(h(x))((g(x)/h(x).

Here.

As

So, y = 0 is the horizontal asymptote.

As the [zeros](https://socratic.org/precalculus/polynomial-functions-

of-higher-degree/zeros) of

vertical asymptotes are

The degree of the numerator is 0 and the the degree of the

denominator is 1 that is higher. So, there is no possibility of another

asymptote,

The two graphs are for the given function and the function that is

obtained after cancelling the common factor

The asymptote y = 0 is also marked in the graphs.

Of course, it was not possible ( for me ) to mark vertical asymptotes, using this utility.

graph{y(y-(2x-2)/((x-1)(x^2+x-1) ))=0[-10, 10, -5, 5]}

graph{y(y-2/(x^2+x-1))=0 [-10, 10, -5, 5]}