claudiaroyer14
claudiaroyer14 claudiaroyer14
  • 10-12-2018
  • Mathematics
contestada

perform the indicated operation a-a^4/a^2+a+1

Respuesta :

meeraasrinivas
meeraasrinivas meeraasrinivas
  • 11-12-2018

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]

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