\(\frac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}\)

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

\(=\frac{\left(x+1\right)\left(x+1\right)}{x\left(x-1\right)+2\left(x-1\right)+\left(x+1\right)}\)

Ddeeff sao rồi bạn ko rút gọn được

a)\(\frac{x^3-x}{3x+3}=\frac{x.\left(x^2-1\right)}{3.\left(x+1\right)}=\frac{x.\left(x-1\right).\left(x+1\right)}{3.\left(x+1\right)}=\frac{x.\left(x+1\right)}{3}=\frac{x^2+x}{3}\)

Bạn có thể giúp mình 2 câu còn lại dc kh ạ 

A) X⁴ - y4 / y3 -x3 = (x²) ² - (y² )² / (y-x)(y^2+xy+x^2)= (x^2-y^2)(x^2+y^2) / (y-x)(y^2+xy+x^2)=-(x-y)(x+y)(x^2+y^2) / (x-y)(x^2+xy+y^2)= - (x+y)(x^2+y^2) / x^2 + xy + y^2

Câu b, bạn nhóm các hạng tử vào vs nhau sẽ xuất hiện nhân tử chung rồi rút gọn đi là ok. Nhóm 2x^3 vs -2x, x^2 vs cộng 1 thì đặt dấu trừ ra ngoài.. Bên dưới nhóm x^3 vs -x,2x^2 vs -2

\(=\frac{\left(x^4-x^3\right)-\left(x-1\right)}{\left(x^4+x^3+x^2\right)+\left(2x^2+2x+2\right)}=\frac{x^3.\left(x-1\right)-\left(x-1\right)}{x^2\left(x^2+x+1\right)+2\left(x^2+x+1\right)}\)

\(=\frac{\left(x^3-1\right).\left(x-1\right)}{\left(x^2+2\right)\left(x^2+x+1\right)}=\frac{\left(x-1\right)^2.\left(x^2+x+1\right)}{\left(x^2+2\right)\left(x^2+x+1\right)}=\frac{\left(x-1\right)^2}{x^2+2}\)

\(\frac{x^4-y^4}{y^3-x^3}=\frac{\left(x^2+y^2\right)\left(x+y\right)\left(x-y\right)}{\left(y-x\right)\left(x^2+xy+y^2\right)}=-\frac{\left(x^2+y^2\right)\left(x+y\right)}{\left(x^2+xy+y^2\right)}\)

\(\frac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}=\frac{2\left(x-2\right)\left(x-3\right)}{\left(x-2\right)3\left(x-3\right)\left(x+3\right)}=\frac{2}{3\left(x+3\right)}\)

\(\frac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}=\frac{\left(x-1\right)\left(x+1\right)\left(2x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}=\frac{2x+1}{x+2}\)

\(\frac{x^4-y^4}{y^3-x^3}=\frac{\left(x^2+y^2\right)\left(x+y\right)\left(x-y\right)}{\left(y-x\right)\left(x^2+xy+y^2\right)}=-\frac{\left(x^2+y^2\right)\left(x+y\right)}{\left(x^2+xy+y^2\right)}\)

\(\frac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}=\frac{2\left(x-2\right)\left(x-3\right)}{\left(x-2\right)3\left(x-3\right)\left(x+3\right)}=\frac{2}{3\left(x+3\right)}\)