Question

Rút gọn biểu thức sau: x³+x²+x+1/3x²+6x+3

Answer 1

\(\frac{x^3+x^2+x+1}{3x^2+6x+3}=\frac{x^2\left(x+1\right)+\left(x+1\right)}{3x^2+3x+3x+3}\)

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

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

Answer 2

\(\frac{x^3+x^2+x+1}{3x^2+6x+3}=\frac{x^2.\left(x+1\right)+\left(x+1\right)}{3.\left(x^2+2x+1\right)}=\frac{\left(x+1\right)\left(x^2+1\right)}{3.\left(x+1\right)^2}=\frac{x^2+1}{3.\left(x+1\right)}\)

Answer 3

\(\frac{x^3+x^2+x+1}{3x^2+6x+3}=\frac{x^2\left(x+1\right)+\left(x+1\right)}{3\left(x^2+2x+1\right)}\)

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