Toán Lớp 8: x^7-x^4+x^3-1/x^6+x^5+x^4+x^2+x+1
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Toán Lớp 8: x^7-x^4+x^3-1/x^6+x^5+x^4+x^2+x+1
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Giải đáp:
[x^7-x^4+x^3-1]/[x^6+x^5+x^4+x^2+x+1]
= [x^7+x^6+x^5 + x^3+x^2+x−x^6−x^5−x^4−x^2−x−1]/[x^6+x^5+x^4+x^2+x+1]
= [x.(x^6+x^5+x^4+x^2+x+1)−(x^6+x^5+x^4+x^2+x+1)]/[x^6+x^5+x^4+x^2+x+1]
= [(x−1).(x^6+x^5+x^4+x^2+x+1)]/[x^6+x^5+x^4+x^2+x+1]
= [(x−1). \cancel{(x^6+x^5+x^4+x^2+x+1)}]/[ \cancel{(x^6+x^5+x^4+x^2+x+1)}]
= x – 1
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$\dfrac{x^7-x^4+x^3-1}{x^6+x^5+x^4+x^2+x+1}$
$=\dfrac{\left(x-1\right)\left(x^2+x+1\right)\left(x^4+1\right)}{x^6+x^5+x^4+x^2+x+1}$
$=\dfrac{\left(x-1\right)\left(x^2+x+1\right)\left(x^4+1\right)}{\left(x^2+x+1\right)\left(x^4+1\right)}$
$=\dfrac{\left(x-1\right)\left(x^4+1\right)}{x^4+1}$
$=x-1$