Question

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

Answer 1

Explanation:

The first step is wrong. It claims that

`(9x^3)/(2x^3+9)=(9x^(\cancel 3))/(2x^(\cancel 3)+9)=(9)/(2+9)`

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

`(9x^3)/(2x^3+9)=\frac{(9)(x^3)}{(2+\textcolor{red}{(9)/(x^3)})(x^3)}=\frac{9}{2+\textcolor{red}{(9)/(x^3)}}`