Rút gọn: 2 x 2 - y 2 3 x + y 2 2 (với x ≥ 0 ; y ≥ 0 ; x ≠ y )
A. 6 x - y
B. 6 x + y
C. 2 3 x - y
D. 2 3 x + y
Rút gọn: x^3 + y^3 - z^3 - 3xyz / (x - y)^2 + (y - z)^2 + (z - x)^2
Rút gọn C= [ (x^2-y^2)^3+(y^2-z^2)^3+(z^2-x^2)^3] / [ (x-y)^3 + (y-z)^3 + (z-x)^3 ]
Rút gọn : (x-y)^3+(y-z)^3+(z-x)^3/(x^2-y^2)^3+(y^2-z^2)^3+(z^2-x^2)^3
Rút gọn phân thức: (x^3 + y^3 + z^3 - 3xyz) / (x - y)^2 + (y - z)^2 + (z - x)^2
\(\frac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
\(=\frac{x^3+y^3+z^3-3xyz}{x^2-2xy+y^2+y^2-2yz+z^2+z^2-2xz+x^2}=\frac{\left(x+y+z\right).\left(x^2+y^2+z^2-xy-yz-zx\right)}{2.\left(x^2+y^2+z^2-xy-yz-zx\right)}=\frac{x+y+z}{2}\)
p/s: áp dụng 7 hàng đẳng thức là làm đc =)
Rút gọn biểu thức
3(x-y)^2-2(x+y)^2-(x-y)(x+y)
Rút gọn : 1+x+x^2+x^3+x^4 / 1+y+y^2+y^3+y^4
Rút gọn M=1+x+x^2+x^3+x^4 ÷ 1+y+y^2+y^3+y^4
rút gọn rồi tính
(x^3+y^3)\(x^2-xy+y^2) tai x=2/3 ;y=1/3
1) rút gọn
a) \(\dfrac{x^2+3x-y^2-3y}{x^2-y^2}=\)
b) \(\dfrac{x^3+3x^2-2}{x^3+3x+4}=\)
\(b,\dfrac{x^3+3x^2-2}{x^3+3x+4}=\dfrac{x^3+x^2+2x^2+2x-2x-2}{x^3+x^2-x^2-x+4x+4}\\ =\dfrac{x^2\left(x+1\right)+2x\left(x+1\right)-2\left(x+1\right)}{x^2\left(x+1\right)-x\left(x+1\right)+4\left(x+1\right)}\\ =\dfrac{\left(x+1\right)\left(x^2+2x-2\right)}{\left(x+1\right)\left(x^2-x+4\right)}=\dfrac{x^2+2x-2}{x^2-x+4}\)
\(a,\dfrac{x^2+3x-y^2-3y}{x^2-y^2}=\dfrac{\left(x^2-y^2\right)+\left(3x-3y\right)}{x^2-y^2}\\ =\dfrac{\left(x-y\right)\left(x+y\right)+3\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\\ =\dfrac{\left(x-y\right)\left(x+y+3\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{x+y+3}{x+y}\)
rút gọn phân thức sau:
(x^3-y^3+z^3+3xyz)/((x+y)^2+(y+z)^2+(z+x)^2)
sai đề rồi nhé , đề phải là :
\(\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
\(=\frac{\left(x-y\right)^3+3xy.\left(x-y\right)+z^3+3xyz}{x^2+2xy+y^2+y^2+2yz+z^2+z^2-2xz+x^2}\)
\(=\frac{\left(x-y+z\right).\left[\left(x-y\right)^2-\left(x-y\right).z+z^2\right]+3xy.\left(x-y+z\right)}{2x^2+2y^2+2z^2+2xy+2yz-2xz}\)
\(=\frac{\left(x-y+z\right).\left(x^2-2xy+y^2-xz+yz+z^2+3xy\right)}{2.\left(x^2+y^2+z^2+xy+yz-xz\right)}\)
\(=\frac{\left(x-y+z\right).\left(x^2+y^2+z^2+xy+yz-xz\right)}{2.\left(x^2+y^2+z^2+xy+yz-xz\right)}\)
\(=\frac{x-y+z}{2}\)