b: \(\dfrac{3xy-3x+2y-2}{y-1}-\dfrac{9x^2-1}{3x-1}\)
=3x+2-3x-1
=1
c: \(=\dfrac{a\left(x-1\right)\left(x+1\right)}{x+1}-\dfrac{ax\left(y+1\right)-a\left(y+1\right)}{y+1}\)
=ax-a-ax+a=0
Chứng minh đẳng thức:
\(\dfrac{a^3-4a^2-a+4}{a^3-7a^2+14a-8}=\dfrac{a+1}{a-2}\)
\(\dfrac{x^2y^2+1+\left(x^2-y\right)\left(1-y\right)}{x^2y^2+1+\left(x^2+y\right)\left(1+y\right)}=\dfrac{y^2-y+1}{y^2+y+1}\)
Rút gọn
a, x4 +x3+x2+x-4/x-1
b, xyz+xy+yz+xz+x+y+z+1/(x+1)(y+1)
c, az+by+bx+ay/a+b
1. rút gọn
a)x^8+x^6 +x^6+x^5+x^4+x^3+x^2+x+1/x^3 -1
b)x^5+x+1/x^3+x^2+x
y^3-x^3/x^3-3x^2y+3xy^2-y^3
Chứng minh các đẳng thức sau :
a) \(\dfrac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}=\dfrac{xy+y^2}{2x-y}\)
b) \(\dfrac{x^2+3xy+2y^2}{x^3+2x^2y-xy^2-2y^3}=\dfrac{1}{x-y}\)
Rút gọn phân thức
a,\(\dfrac{\left(x^2-y\right).\left(y+1\right)+x^2y^2-1}{\left(x^2+y\right).\left(y+1\right)+x^2y^2+1}\)
b,\(\dfrac{x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x+y\right)}{x^2y-x^2z+y^2z-y^3}\)
c, \(\dfrac{x^3+3x^2-4}{x^3-3x+2}\)
d , \(\dfrac{x^4+6x^3+9x^2-1}{x^4+6x^3+7x^2-6x+1}\)
Chứng minh đẳng thức:
a, \(\left(\dfrac{3}{2x-y}-\dfrac{2}{2x+y}-\dfrac{1}{2x-5y}\right).\dfrac{4x^2-y^2}{y^2}=\dfrac{-24}{2x-5y}\)
b, \(\dfrac{x^2-x+1}{x^2+x}.\dfrac{x+1}{3x-2}.\dfrac{9x-6}{x^2-x+1}=\dfrac{3}{x}\)
cho biểu thức
A=(\(\dfrac{x+y}{1-xy}\)+\(\dfrac{x-y}{1+xy}\)) : (\(\dfrac{x^2+y^2+2x^2y^2}{1-x^2-y^2}\)+1) với x y khác 1
a) Rút gọn A
b) tìm các số nguyên ko âm x để A thuộc Z
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)\(\dfrac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
a.3x(1-x)/2(x-1) b.6x²y²/8xy⁵ c.3(x-y)(x-z)²/x-y)(x-z)
