ANSWER
[tex]\frac{ - 12}{1 + 8x} [/tex]
EXPLANATION
The given rational expression is
[tex] \frac{ - 12 {x}^{4} }{ {x}^{4} + 8 {x}^{5} } [/tex]
We factor to get;
[tex]\frac{ - 12 {x}^{4} }{ {x}^{4} (1+ 8 {x}) } [/tex]
We can see that:
[tex] {x}^{4} [/tex]
is common to both the numerator and the denominator.
We cancel out the common factors to obtain;
[tex]\frac{ - 12 }{ 1+ 8 {x}} [/tex]
Therefore the simplified form is
[tex] \frac{ - 12}{1 + 8x} [/tex]
