If someone could explain the error in depth and show step by step how to actually slove the problem that would be great.

Step-by-step explanation:

The first step is wrong. It claims that

but it is not true. It is attempting to simplify the fraction by cancelling the x^3 terms from 9x^3 and 2x^3.

However, to perform this operation, all terms in the fraction must be divided by x^3. But this will mean

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.