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) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
Rút gọn các biểu thức sau :
a)\(\dfrac{25xy^3\left(2x-y\right)^2}{75xy^2\left(y-2x\right)}\)
b)\(\dfrac{x^2-y^2}{x^2-y^2+xz-yz}\)
c)\(\dfrac{\left(2x+3\right)-x^2}{x^2-1}\)
d)\(\dfrac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
Rút gọn, rồi tính giá trị các phân thức sau : A=\(\dfrac{\left(2x^{2^{ }}+2x^{ }\right)\left(x-2\right)^2}{^{ }\left(x^{3^{ }}-4x\right)\left(x+1\right)}\)với x = \(\dfrac{1}{2}\)
B=\(\dfrac{x^3-x^{2^{ }}y+xy^2}{x^3+y^3}\)với x = -5 , y = 10
Rút gọn phân thức :
a) \(\dfrac{x^4-y^4}{y^3-x^3}\)
b) \(\dfrac{\left(2x-4\right)\left(x-3\right)}{\left(x-2\right)\left(3x^2-27\right)}\)
c) \(\dfrac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}\)
Rút gọn các phân thức sau:
a) \(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
b) \(\dfrac{\left(2x^2+2x\right)\left(x-2\right)^2}{\left(x^3-4x\right)\left(x+1\right)}\)
c) \(\dfrac{x^3-x^2y+xy^2}{x^3+y^3}\)
d) \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\)
e) \(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)
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 các phân thức sau :
a) \(\dfrac{x^2-16
}{4x-x^2}\) ( x \(\ne\) x , x \(\ne\) 4 )
b) \(\dfrac{x^2+4x+3}{2x+6}\) ( x \(\ne\) -3 )
c) \(\dfrac{15x\left(x+y\right)^3}{5y\left(x+y\right)^2}\) ( y + ( x + y ) \(\ne\) 0 )
d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}\) ( x \(\ne\) y )
e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}\) ( x \(\ne\) - y )
f)\(\dfrac{x^2-xy}{3xy-3y^2}\) ( x \(\ne\) y , y \(\ne\) 0 )
g) \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\) ( b \(\ne\) 0 , x \(\ne\pm\)1 )
h) \(\dfrac{4x^2-4xy}{5x^3-5x^2y}\left(x\ne0,x\ne y\right)\)
i) \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\left(x+y+z\ne0\right)\)
k)\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\left(x\ne0,x\ne y\right)\)
Help me!!!
1. Tìm giá trị của x để các phân thức sau = 0 .
a) \(\dfrac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}\)
b)\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}\)
2. Rút gọn các phân thức :
a) \(\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
b) \(\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)
c) \(\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+x\right)^2+\left(z-x\right)^2}\)
d)\(\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
Rút gọn các phân thức :
\(A=\dfrac{x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)}{xy^2-xz^2-y^3+yz^2}\)
\(B=\dfrac{a^3-b^3+c^3+3abc}{\left(a+b\right)^2+\left(b-c\right)^2+\left(c+a\right)^2}\)
\(C=\dfrac{a^3b-ab^3+b^3c-bc^3+c^3a-ca^3}{a^2b-ab^2+b^2c-bc^2+c^2a-ca^2}\)
