Question

Rút gọn phân thức rồi tính A tại x = 2

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

Answer 1

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

\(=\dfrac{2\left(2^6+2^5+2^4+2^3+2^2+2+1\right)}{\left(2-1\right)\left(2+1\right)\left(2^2+1\right)}\)

\(=\dfrac{2\cdot\left(2^7-1\right)}{3\cdot5}=\dfrac{254}{15}\)