(ax-b) / (cx-d) maximum Such as the title And what does the function image look like?

(ax-b) / (cx-d) maximum Such as the title And what does the function image look like?

When x tends to infinity, there is a minimum a / C
When x tends to D / C, there is an infinite maximum
The original function can be reduced to y = A / C + (D / C-B / a) / (X-D / C)
You can expand (D / C-B / a) times from y = 1 / x [the general trend of the image does not change], then shift D / C to the right, and finally shift a / C upward to get the image of the original function. That is to say, the image is actually a hyperbola. When x tends to D / C, y tends to infinity, and when x tends to infinity, y tends to a / C

The same factor of x ^ 2-16, x ^ 2 + 4-4x is ax ^ 2 + 4 BX ^ 2-4 CX + 2 dx-2
that
I just asked the wrong question
It should be the same factor of x ^ 4-16, x ^ 2 + 4-4x

x²-16=(x-4)(x+4)
x²+4-4x=(x-2)²
There is no same factor for x ^ 2-16, x ^ 2 + 4-4x
Is the title wrong