<s>[INST] Simplifying algebraic expression with fraction of polynomials I cannot seem to find a way to simplify the following expression:
$$\frac{9{a}^{4}-{a}^{2}{ b  }^{ 4  }  +16 { b  }^{ 8  }    }{ 3 { a  }^{ 2  }  -5a { b  }^{ 2  }  +4 { b  }^{ 4  }    }$$
I have tried factoring by $a$ and rewriting the division as multiplication with inverse.
 [/INST] A straightforward solution, simply use long division.
\begin{array}{rrrrrrr}
& & 3a^2 &+5a b^2&+4b^4&&\\
\hline
3a^2-5ab^2+4b^4 & | & 9a^4 & & -a^2b^4 &&+ 16 b^8\\
&&-9a^4&+15a^3b^2&-12a^2b^4\\
\hline
&&&15a^3b^2&-13a^2b^4&&+16b^8\\
&&&-15a^3b^2&+25a^2b^4&-20ab^6\\
\hline
&&&&12a^2b^4&-20a b^6&+16b^8\\
&&&&-12a^2b^4&+20ab^6&-16b^8\\
\hline
&&&&&&0
\end{array}
</s>