Given the following function $R(x)$ [in pic] find the vertical, horizontal, oblique asymptotes. In order to find the asymptotes you need to reduce the function, so I did the following:
This is incorrect, the solution is $(2x-3)$; I noticed that the x method/ diamond method did not work here since the factors $(2x-3)(4x+7)$ did not multiply to $4x^2+x-21/2$ but rather $8x^2 +2x-21$, how this happens I do not know. Now, I understand there are many other ways of factoring this problem but I seem to have either made a mistake somewhere or have found a situation where the criss cross method does not work? I would like help finding out exactly what I did wrong, to help strengthen my math foundation.
You are incorrect in the following part:
$$8x^2+2x-21\ne 2(4x+7)(2x-3)$$
There is another part where you without reason, just add another $2$ also.
The correct factoring should be:$$R(x)=2x-3, \text{ where } x\ne-\dfrac{7}{4}$$