Question

How do you simplify `(t^3+8)/(3t^2+t-10)`?

Answer 1

`color(blue)(1/3t-1/9+[color(white)(.)(31t+92)/(27t^2+9t-90) color(white)(.)]`

Explanation:

Write `t^3+8" as "t^3+0t^2+0t+8` for simplicity of comparison

The `0t^2" and "0t` have no value. They are just 'place holders' to make formatting of this solution easier.

`" "t^3+0t^2+0t+8`
`color(red)(1/3t)(3t^2+t-10) -> " "ul(t^3+1/3t^2-10/3t)" "larr" Subtract"`
`" "0-1/3t^2+10/3t+8`
`color(red)(-1/9)(3t^2+t-10) ->" " ul(-1/3t^2-1/9t+10/9 ) " "larr" Subtract"`
`color(red)(" Remainder" -> 0+31/9t+92/9)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)(1/3t-1/9+[color(white)(.)(31t+92)/9 -:(3t^2+t-10)color(white)(.)]`

`color(blue)(1/3t-1/9+[color(white)(.)(31t+92)/(27t^2+9t-90) color(white)(.)]`