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

Step-by-step explanation:

The first step is wrong. It claims that

$\frac{9x^3}{2x^3+9}=\frac{9x^{\cancel 3}}{2x^{\cancel 3}+9}=\frac{9}{2+9}$

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

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