Question

Cho biểu thức A=\(\frac{x}{x+1}-\frac{3-3x}{x^2-x+1}+\frac{x+4}{x^3+1}\)

a) Rút gọn biểu thức A

Answer 1

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