Question

Thu gọn:

\(\dfrac{x^3+8}{x^2+2x}\) ; \(\dfrac{x^2+2x+1}{x^3+1}\)

Answer 1

\(\dfrac{x^3+8}{x^2+2x}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x\left(x+2\right)}=\dfrac{x^2-2x+4}{x}=\dfrac{\left(x-1\right)^2+3}{x}\)

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

Answer 2

\(\dfrac{x^3+8}{x^2+2x}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x\left(x+2\right)}=\dfrac{x^2-2x +4}{x}\)

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