Bài 2: Rút gọn các phân thức: a) (x-x^2)/(x^2)-1 b) (x^2+2x+1)/(5x^3)+5x^(2) c) (y^2-x^2)/(x^2)-3xy+2y^(2) d) (x^2y+2xy^2+y^3)/(2x^2)+xy-y^(2) e) (9-(x+5)^2)/(x^2)+4x+4 f) (x^2+5x+6)/(x^2)+4x+4 g) (3x^2+5x-2)/(x^2)-3x-10 h) (x^2+y^2-1+2xy)/(x^2)-y^(2+1+2x) i) (a^2+b^2-c^2+2ab)/(a^2)-b^(2+c^2+2ac) k) (y^2-x^2)/(x^3)-3x^(2y+3xy^2-y^3) 1) (x^2+3xy+2y^2)/(x^3)+2x^(2y-xy^2-2y^3)

a) $\frac {x-x^{2}}{x^{2}-1} = \frac {x(1-x)}{(x-1)(x+1)} = \frac {x}{x+1}$<br /><br />b) $\frac {x^{2}+2x+1}{5x^{3}+5x^{2}} = \frac {(x+1)^2}{5x^2(x+1)} = \frac {x+1}{5x^2}$<br /><br />c) $\frac {y^{2}-x^{2}}{x^{2}-3xy+2y^{2}} = \frac {(y-x)(y+x)}{(x-y)(x-2y)} = \frac {y+x}{x-2y}$<br /><br />d) $\frac {x^{2}y+2xy^{2}+y^{3}}{2x^{2}+xy-y^{2}} = \frac {y(x^2+2xy+y^2)}{y(2x^2+x-y)} = \frac {x^2+2xy+y^2}{2x^2+x-y}$<br /><br />e) $\frac {9-(x+5)^{2}}{x^{2}+4x+4} = \frac {9-(x^2+10x+25)}{x^2+4x+4} = \frac {-x^2-10x-16}{x^2+4x+4} = -\frac {x^2+10x+16}{x^2+4x+4}$<br /><br />f) $\frac {x^{2}+5x+6}{x^{2}+4x+4} = \frac {(x+2)(x+3)}{(x+2)(x+2)} = \frac {x+3}{x+2}$<br /><br />g) $\frac {3x^{2}+5x-2}{x^{2}-3x-10} = \frac {3x^2+5x-2}{(x-5)(x+2)}$<br /><br />h) $\frac {x^{2}+y^{2}-1+2xy}{x^{2}-y^{2}+1+2x} = \frac {(x+y)^2-1}{(x+y)^2-1} = 1$<br /><br />i) $\frac {a^{2}+b^{2}-c^{2}+2ab}{a^{2}-b^{2}+c^{2}+2ac} = \frac {(a+b)^2-c^2}{(a-b)^2+c^2} = \frac {a+b}{a-b}$<br /><br />k) $\frac {y^{2}-x^{2}}{x^{3}-3x^{2}y+3xy^{2}-y^{3}} = \frac {(y-x)(y+x)}{(x-y)(x^2-3xy+3y^2)} = \frac {y+x}{x^2-3xy+3y^2}$<br /><br />1) $\frac {x^{2}+3xy+2y^{2}}{x^{3}+2x^{2}y-xy^{2}-2y^{3}} = \frac {(x+y)^2}{x^2(x+2y)-y(x+2y)} = \frac {x+y}{x^2-y}$