Question

Rút gọn phân thức :

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

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

3) \(\frac{9x^2y^2+3x^2}{12xy^5+4xy^3}\)

Answer 1

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

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

c)

\(\frac{9x^2y^2+3x^2}{12xy^5+4xy^3}=\frac{3x^2\left(3y^2+1\right)}{4xy^3\left(3y^2+1\right)}=\frac{3x^2}{4xy^3}\)

@@@@ỦNG HỘ NHOA@@@@

Answer 2

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