simplify expression: [(2x^3)/(x - 2)]/[(6x^2)/(x^3 - 8)]

[snakeyesxlaw]

((2 x^3)/(x - 2))
--------------------------
((6 x^2)/(x^3 - 8))

= ((2x^3)/(x-2)) * ((x^3-8)/(6x^2))

= (x/(x-2)) * ((x^3-8)/3)

= (x(x^3-8)) / 3

= (x^3 - 4x^2 + 4x) / 3

where did this go wrong?

 

[ilaggoodly]

\(\displaystyle \L \frac{x}{x-2} \cdot \frac{x^3-8}{3}\)

through synthetic division, you may notice that (x-2)goes into x^3-8
so thats

\(\displaystyle \L \frac{x}{1} \cdot \frac{x^2+2x+4}{3}\)

\(\displaystyle \L \frac{x^3+2x^2+4x}{3}\)

something weird happened to your x-2