Rút gọn phân thức:
1, \(\dfrac{x^2+y^2-1+2xy}{x^2-y^2+1+2x}\)
2, \(\dfrac{x^4-y^4}{x^3+y^3}\)
3, \(\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(x-z\right)^2+\left(y-z\right)^2}\)
4, \(\dfrac{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}{\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3}\)
5, \(\dfrac{x^3-7x+6}{x^2\left(x-3\right)^2+4x\left(3-x\right)^2+4\left(x-3\right)^2}\)

Rút gọn:
a) \(\dfrac{3\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}\)
b) \(\dfrac{6x^2y^2}{8xy^5}\)
c) \(\dfrac{3x\left(1-x\right)}{2\left(x-1\right)}\)
d) \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)
e) \(\dfrac{x^2-2x+1}{x^2-1}\)
f) \(\dfrac{8x-4}{8x^3-1}\)
g) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
k) \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)

Rút gọn phân thức:

1.\(\dfrac{\left(x-y\right)^{3^{ }}-3xy\left(x+y\right)+y^3}{x-6y}\)

2. \(\dfrac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}\)

3.\(\dfrac{\left(n+1\right)!}{n!\left(n+2\right)}\)

4. \(\dfrac{n!}{\left(n+1\right)!-n!}\)

5. \(\dfrac{\left(n+1\right)!-\left(n+2\right)!}{\left(n+1\right)!+\left(n+2\right)!}\)

Rút gọn các biểu thức sau : 

A = \(2x^2\left(-3x^3+2x^2+x-1\right)+2x\left(x^2-3x+1\right)\)

B = \(2x:\dfrac{1}{2}x+x^2\)

C = \(\left[1:\left(1+x\right)+2x:\left(1-x^2\right)\right]:\left(\dfrac{1}{x}-1\right)\)

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

E = \(\dfrac{\left|x-3\right|}{x^2-9}.\left(x^2+6x+9\right)\)

F = \(\dfrac{\sqrt{x}}{\sqrt{x}-5}-\dfrac{10\sqrt{x}}{x-25}-\dfrac{5}{\sqrt{x}+5}\)

Rút gọn các biểu thức sau : 

A = \(2x^2\left(-3x^3+2x^2+x-1\right)+2x\left(x^2-3x+1\right)\)

B = \(2x:\dfrac{1}{2}x+x^2\)

C = \(\left[1:\left(1+x\right)+2x:\left(1-x^2\right)\right]:\left(\dfrac{1}{x}-1\right)\)

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

E = \(\dfrac{\left|x-3\right|}{x^2-9}.\left(x^2+6x+9\right)\)

F = \(\dfrac{\sqrt{x}}{\sqrt{x}-5}-\dfrac{10\sqrt{x}}{x-25}-\dfrac{5}{\sqrt{x}+5}\)

Bài `1`: Rút gọn các biểu thức sau:

\(a)4x^2\left(5x^2+3\right)-6x\left(3x^3-2x+1\right)-5x^3\left(2x-1\right)\)

\(b)\dfrac{3}{2}x\left(x^2-\dfrac{2}{3}x+2\right)-\dfrac{5}{3}x^2\left(x+\dfrac{6}{5}\right)\)

Bài `2`: Thực hiện các phép nhân sau:

\(a)\left(x^2-x\right)\cdot\left(2x^2-x-10\right)\)

\(b)\left(0,2x^2-3x\right)\cdot5\left(x^2-7x+3\right)\)

\(c)6x^2\cdot\left(2x^3-3x^2+5x-4\right)\)

\(d)\left(-1,2x^2\right)\cdot\left(2,5x^4-2x^3+x^2-1,5\right)\)

1. Cho biết x , y , z # 0 và \(\dfrac{\left(ax+by+cz\right)^2}{x^2+y^2+z^2}=a^2+b^2+c^2\) .
Chứng minh rằng : \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
2. Rút gọn : \(\dfrac{x^2+y^2+z^2}{\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2}\) , biết rằng : x + y + z = 0
3. Cho 3x - y = 3z và 2x + y = 7z . Tính giá trị cua biểu thức :
M = \(\dfrac{x^2-2xy}{x^2+y^2}\) ( x # 0 ; y # 0 )