По формулам:
(3x)³-1=(3x-1)·(9x²+3x+1) ⇒ 9x²+3x+1 = ((3х)³-1)/(3х-1)
(9x²)³-1=(9x²-1)·(81x⁴+9x²+1) ⇒81x⁴+9x²+1 =
= ((9x²)³-1)/(9x²-1) = (((3x)³)²-1)/(3x-1)(3x+1)= ((3x)³-1)((3x)³+1)/(3x-1)(3x+1)
Поэтому
(81x⁴+9x²+1)/( 9x²+3x+1)=((3x)³-1)((3x)³+1)/(3x-1)(3x+1) : ((3х)³-1)/(3х-1) =
=((3x)³+1)/(3x+1)=(9x^2-3x+1)
Copyright © 2025 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Verified answer
По формулам:
(3x)³-1=(3x-1)·(9x²+3x+1) ⇒ 9x²+3x+1 = ((3х)³-1)/(3х-1)
(9x²)³-1=(9x²-1)·(81x⁴+9x²+1) ⇒81x⁴+9x²+1 =
= ((9x²)³-1)/(9x²-1) = (((3x)³)²-1)/(3x-1)(3x+1)= ((3x)³-1)((3x)³+1)/(3x-1)(3x+1)
Поэтому
(81x⁴+9x²+1)/( 9x²+3x+1)=((3x)³-1)((3x)³+1)/(3x-1)(3x+1) : ((3х)³-1)/(3х-1) =
=((3x)³+1)/(3x+1)=(9x^2-3x+1)