Rút gọn các phân thức :

a) \(\dfrac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)

b) \(\dfrac{8xy\left(3x-1\right)^3}{12x^3\left(1-3x\right)}\)

c) \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)

d) \(\dfrac{5x^2-10xy}{2\left(2y-x\right)^3}\)

e) \(\dfrac{32x-8x^2+2x^3}{x^3+64}\)

f) \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)

g) \(\dfrac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)

h) \(\dfrac{5x^3+5x}{x^4-1}\)

i) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)

Quy đồng mẫu thức các phân thức sau :

a) \(\dfrac{25}{14x^2y};\dfrac{14}{21xy^5}\)

b) \(\dfrac{11}{102x^4y};\dfrac{3}{34xy^3}\)

c) \(\dfrac{3x+1}{12xy^4};\dfrac{y-2}{9x^2y^3}\)

d) \(\dfrac{1}{6x^3y^2};\dfrac{x+1}{9x^2y^4};\dfrac{x-1}{4xy^3}\)

e) \(\dfrac{3+2x}{10x^4y};\dfrac{5}{8x^2y^2};\dfrac{2}{3xy^5}\)

f) \(\dfrac{4x-4}{2x\left(x+3\right)};\dfrac{x-3}{3x\left(x+1\right)}\)

g) \(\dfrac{2x}{\left(x+2\right)^3};\dfrac{x-2}{2x\left(x+2\right)^2}\)

h) \(\dfrac{5}{3x^3-12x};\dfrac{3}{\left(2x+4\right)\left(x+3\right)}\)

bài 1. rút gọn phân thức sau :

a, \(\dfrac{15xy}{10x^2y}\)

b, \(\dfrac{4\left(2-x\right)}{6x\left(x-2\right)}\)

c, \(\dfrac{12x^3\left(x-4\right)^2}{8x^2\left(4-x\right)}\)

d, \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)

bài 2. rút gọn phân thức sau :

a, \(\dfrac{15\left(x-3\right)^3}{9-3x}\)

b, \(\dfrac{4\left(5x-1\right)^3}{2-10x}\)

c,\(\dfrac{9x^2y}{-15x^3y}\)

d, \(\dfrac{-15x\left(x-y\right)^2}{6x^2\left(x-y\right)^3}\)

bài 3. rút gọn phân thức sau :

a, \(\dfrac{5x^2+10x+5}{11x+11}\)

b, \(\dfrac{18x+6x^2+2x^3}{x^3-27}\)

c, \(\dfrac{12x^2+12x+3}{4x^2-1}\)

bài 4 : rút gọ phân thức đại số

A= \(\dfrac{12xy^2}{-9x^3y}\)

B=\(\dfrac{35xy\left(x-4\right)^2}{28x^2\left(4-x\right)}\)

C= \(\dfrac{6x+18y}{x^2-9y^2}\)

Thực hiện phép tính:
a) \(\dfrac{2}{5}xy\left(x^2y-5x+10y\right)\)
b) \(\left(x^2-1\right)\left(x^2+2x+y\right)\)
c) \(\left(x+3y\right)^2\)
d) \(\left(4x-y\right)^3\)
e) \(\left(x^2-2y\right)\left(x^2+2y\right)\)
g) \(18x^4y^2z:10x^4y\)
h) \(\left(x^3y^3+\dfrac{1}{2}x^2y^3-x^3y^2\right):\dfrac{1}{3}x^2y^2\)
i) \(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\)
k) \(\dfrac{5x-1}{3x^2y}+\dfrac{x+1}{3x^2y}\)
l) \(\dfrac{3x+1}{x^2-3x+1}+\dfrac{x^2-6x}{x^2-3x+1}\)
m) \(\dfrac{2x+3}{10x-4}+\dfrac{5-3x}{4-10x}\)
n) \(\dfrac{x}{x^2+2x+1}+\dfrac{3}{5x^2-5}\)
o) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
p) \(\dfrac{4x+2}{15x^3y}\dfrac{5y-3}{9x^2y}+\dfrac{x+1}{5xy^3}\)
q) \(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
r) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
x) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)\)
y) \(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\)
z) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)
t) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
w) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)

RÚT GỌN PHÂN THỨC:  

 a) \(\frac{4x^3}{10x^2y}\)                       b) \(\frac{10xy^5\left(2x-3y\right)}{12xy\left(2x-3y\right)}\)

c)   \(\frac{x^2+2x+1}{5x^3+5x^2}\)                                d)     \(\frac{2x^2+2x}{x+1}\)

e)    \(\frac{3\left(x-y\right)}{y-x}\)

f)  \(\frac{x^2-x}{1-x}\)