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

Jul 9, 2016

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

#### Explanation:

Write ${t}^{3} + 8 \text{ as } {t}^{3} + 0 {t}^{2} + 0 t + 8$ for simplicity of comparison

The $0 {t}^{2} \text{ and } 0 t$ have no value. They are just 'place holders' to make formatting of this solution easier.

$\text{ } {t}^{3} + 0 {t}^{2} + 0 t + 8$
$\textcolor{red}{\frac{1}{3} t} \left(3 {t}^{2} + t - 10\right) \to \text{ "ul(t^3+1/3t^2-10/3t)" "larr" Subtract}$
$\text{ } 0 - \frac{1}{3} {t}^{2} + \frac{10}{3} t + 8$
$\textcolor{red}{- \frac{1}{9}} \left(3 {t}^{2} + t - 10\right) \to \text{ " ul(-1/3t^2-1/9t+10/9 ) " "larr" Subtract}$
$\textcolor{red}{\text{ Remainder} \to 0 + \frac{31}{9} t + \frac{92}{9}}$
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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)(.)]