Rút gọn \(P=\frac{x^8+x^7+x^6+x^5+x^4-x^3+x^2+x+3}{x^3-1}\)
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Bài 2:
a: 2/6x5/3=10/18=5/9
b: 11/9x5/10=55/90=11/18
c: 3/9x6/8=1/3x3/4=1/4
d: 4/9x12/16=48/144=1/3
e: 25/15x6/7=5/3x6/7=30/21=10/7
f: 6/10x15/20=90/200=9/20
Bài 1
4/5 x 6/7= 24/35
2/9 x 1/2= 2/18= 1/9
1/2 x 8/3= 8/6= 4/3
7/9 x 6/5= 42/45= 14/15
8/7 x 5/9= 40/63
10/11 x 22/15= 220/165= 4/3
Bài 2
2/6 x 5/3= 1/3 x 5/3=5/9
11/9 x 5/10= 11/9 x 1/2= 11/18
3/9 x 6/8= 1/3 x 3/4 =3/12= 1/4
4/9 x 12/16= 4/9 x 3/4= 12/36= 1/3
25/15 x 6/7= 5/3 x 6/7= 30/21= 10/7
6/10 x 15/20= 3/5 x 3/4= 9/20
\(\frac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^2-1}\left(DK:x\ne-1;x\ne1\right)\)
\(=\frac{x^4\left(x^3+x^2+x+1\right)+\left(x^3+x^2+x+1\right)}{x^2-1}\)
\(=\frac{x^4\left[x\left(x^2+1\right)+x^2+1\right]+\left[x\left(x^2+1\right)+x^2+1\right]}{x^2-1}\)
\(=\frac{\left(x^4+1\right)\left(x+1\right)\left(x^2+1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{\left(x^2+1\right)\left(x^4+1\right)}{x-1}\)
\(\frac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^2-1}\)
\(=\frac{x^6\left(x+1\right)+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{\left(x+1\right)\left(x^6+x^4+x^2\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x^6+x^4+x^2}{x+1}\)
\(=\frac{x^2\left(x^3+x^2+1\right)}{x+1}\)