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\(\dfrac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^2-1}\)
\(=\dfrac{x^6\left(x+1\right)+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x^6+x^4+x^2+1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^4\left(x^2+1\right)+\left(x^2+1\right)}{x-1}=\dfrac{\left(x^2+1\right)\left(x^4+1\right)}{\left(x-1\right)}\)
Chúc bạn học tốt!!!
a: \(A=\dfrac{x-1+2x^2+2x+2-x^2-2x}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x-1}\)
Gọi phân thức cần tìm là \(A\)
Ta có:
\(\dfrac{1}{x}.\dfrac{x}{x+1}.\dfrac{x+1}{x+2}.\dfrac{x+2}{x+3}.\dfrac{x+3}{x+4}.\dfrac{x+4}{x+5}.\dfrac{x+5}{x+6}.\dfrac{x+6}{x+7}.\dfrac{x+7}{x+8}.\dfrac{x+8}{x+9}.\dfrac{x+9}{x+10}\)
\(=\dfrac{x\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)\left(x+7\right)\left(x+8\right)\left(x+9\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)\left(x+7\right)\left(x+8\right)\left(x+9\right)\left(x+10\right)}\)\(=\dfrac{x}{x+10}\)
Suy ra:
\(\dfrac{1}{x}.\dfrac{x}{x+1}.\dfrac{x+1}{x+2}.\dfrac{x+2}{x+3}.\dfrac{x+3}{x+4}.\dfrac{x+4}{x+5}.\dfrac{x+5}{x+6}.\dfrac{x+6}{x+7}.\dfrac{x+7}{x+8}.\dfrac{x+8}{x+9}.\dfrac{x+9}{x+10}.A=1\)
\(\Leftrightarrow\dfrac{x}{x+10}.A=1\)
\(\Leftrightarrow A=\dfrac{x+10}{x}\)
Vậy phân thức cần điền vào chỗ trống là \(\dfrac{x+10}{x}\)
Trả lời:
M = ( x - 3 )3 - ( x + 1 )3 - 12x ( x - 1 )
= x3 - 3.x2.3 + 3.x.32 - 33 - ( x3 + 3.x2.1 + 3.x.12 + 13 ) - 12x2 - 12x
= x3 - 9x2 + 27x - 27 - x3 - 3x2 - 3x - 1 - 12x2 - 12x
= - 24x2 + 12x - 28
a) \(=12y^2+3y+28-12y^2=3y+28\)
b) \(=x^2-4x+4-3x^2+8x+3=-2x^2+4x+7\)
Ta có :\(\frac{x^7+x^6+x^5+x^4+x^3+x^2+1}{x^2-1}\)
\(=\frac{x^6\left(x+1\right)+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)}{x^2-1}\)
\(=\frac{\left(x^6+x^4+x^2+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{\left(x^6+x^4+x^2+1\right)}{\left(x-1\right)}\)