Сократите дробь ( : - знак дроби ) 9x^5-40x^3+16x : 3x^4 - 8x^3 + 4x^2

Question

Сократите дробь ( : - знак дроби )
9x^5-40x^3+16x : 3x^4 - 8x^3 + 4x^2

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Answer 1

9x^5-40x³+16x=x(9x^4-40x²+16)=9x(x²-4/9)(x²+32/9)=x(x-2/3)(x+2/3)(9x²+32)
9x^4-40x²+16=9(x²-4/9)(x²+32/9)
x²=a
9a²-40a+16=0
D=1600-576=1024
a1=(40-32)/18=4/9 U a2=((40+32)/18=32/9

3x^4-8x³+4x²=x²(3x²-8x+4)=3x(x-2/3)(x-2)
D=64-48=16
x1=(8-4)/6=2/3 U x2=(8+4)/6=2

(9x^5-40x³+16x)/(3x^4-8x³+4x²)=x(x-2/3)(x+2/3)(9x²+32)/3x²(x-2/3)(x-2)=
=(3x+2)(9x²+32)/9x(x-2)