Question

Đố em rút gọn được phân thức:

\(\dfrac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^2-1}\)

GIẢI THÍCH RÕ RÀNG GIÚP MK VS NHÉ! HELP ME!!!!!!!!!

Answer 1

\(\dfrac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^2-1}\)

\(=\dfrac{x^6\left(x+1\right)+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\)

\(=\dfrac{\left(x+1\right)\left(x^6+x^4+x^2+1\right)}{\left(x+1\right)\left(x-1\right)}\)

\(=\dfrac{x^4\left(x^2+1\right)+\left(x^2+1\right)}{x-1}=\dfrac{\left(x^2+1\right)\left(x^4+1\right)}{\left(x-1\right)}\)

Chúc bạn học tốt!!!