Answer:
[tex]\frac{a-a^{4}}{a^{2}+a+1} =-a^{2}+a[/tex]
Step-by-step explanation:
Factorizing the numerator:
a- a⁴ = -a(a³ - 1)
W.k.t., (a³-b³) =(a-b)(a²+ab+b²)
So, (a³-1) = (a-1)(a²+a+1)
Now, (a-a⁴) = -a(a-1)(a²+a+1)
We have
[tex]\frac{a-a^{4}}{a^{2}+a+1} =\frac{-a(a-1)(a^{2}+a+1)}{a^{2}+a+1} =-a(a-1) =-a^{2}+a[/tex]
∴[tex]\frac{a-a^{4}}{a^{2}+a+1} =-a^{2}+a[/tex]