a: \(=\left(2x-y\right)\left(x+y+3x-y\right)+\left(2x-y\right)\)

\(=\left(2x-y\right)\left(4x+1\right)\)

b: \(=abc\left(b^2c-abc+bc^2-a\right)\)

d: \(=x^2\left(2x+3\right)+2x+3=\left(2x+3\right)\left(x^2+1\right)\)

a)\(\left(x+y+z\right)\left(x^2-xy+y^2\right)\)

b),c) sai đề

Dấu * là gì vậy ạ?

Nhân chứ gì

a) \(=\left(x-5\right)\left(2+x+5-2x-1\right)=\left(x-5\right)\left(6-x\right)\)

e) \(=\left(ab^3c^2-a^2b^2c^2\right)+\left(ab^2c^3-a^2bc^3\right)=ab^2c^2\left(b-a\right)+abc^3\left(b-a\right)=abc^2\left(b-a\right)\left(b+c\right)\)

ChươngII *Dạng toán rútg gọn phân thức

Bài 1.Rút gọn phân thức

a. \(\dfrac{3x\left(1-x\right)}{2\left(x-1\right)}=\dfrac{-3x\left(x-1\right)}{2\left(x-1\right)}=-\dfrac{3x}{2}\)

b.\(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x.2xy^2}{4y^3.2xy^2}=\dfrac{3x}{4y^3}\)

c.\(\dfrac{23\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}=\dfrac{23\left(x-z\right)}{6}\)

Bài 2 rút gọn các phân thức sau:

a.\(\dfrac{x^2-16}{4x-x^2}=\dfrac{\left(x-4\right)\left(x+4\right)}{-x\left(x-4\right)}=-\dfrac{x+4}{x}\)(x khác 0,x khác 4)

b.\(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

( x \(\ne-3\) )

c.\(\dfrac{15x\left(x+y\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+y\right)}{y}\) (y+(x+y) khác 0)

d. \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{4}{5}\)

(x khác y)

e.\(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)

(x khác -y)

f.\(\dfrac{x^2-xy}{3xy-3y^2}=\dfrac{x\left(x-y\right)}{3y\left(x-y\right)}=\dfrac{x}{3y}\)(x khác y,y khác 0)

g.\(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}=\dfrac{2a\left(x^2-2x+1\right)}{-5b\left(x^2-1\right)}=\dfrac{2a\left(x-1\right)^2}{-5b\left(x-1\right)\left(x+1\right)}=\dfrac{2a\left(x-1\right)}{-5b\left(x+1\right)}\)

\ (b khác 0,x khác +-1)

h. \(\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4x}{5x^2}\)

(x khác 0,x khác y)

i.\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)

(x+y+z khác 0)

k.\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}=\dfrac{\left(x^3\right)^2+2x^3y^3+\left(y^3\right)^2}{x\left(x^6-y^6\right)}=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x^3+y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)

(x khác 0,x khác +-y)