Hãy tìm giá trị nhỏ nhất
a)\(B=\left(\dfrac{x^2-2x+2011}{x^2}\right)\)(x khác 0 )
b)\(C=\left(\dfrac{2x+1}{x^2+2}\right)\)
c)D=\(\dfrac{1}{x^2+y^2}+\dfrac{3}{4xy}\) và \(E=\dfrac{1}{x^2+y^2}+\dfrac{1}{xy}\) nếu \(\left\{{}\begin{matrix}x+y=1\\x>0;y>0\end{matrix}\right.\)
d)M=\(x^4+y^4\) và \(N=x^8+y^8\) nếu x+y=2
Thực hiện phép tính:
a) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\)
b) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
c) \(\dfrac{xy}{ab}+\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}-\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)
d) \(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
thuc hien phep tinh
a.\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b.\(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+1-2\right)\)
c.\(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
d.\(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Thực hiện các phép tính :
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)
c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Thực hiên phép tính:
a) \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}+\dfrac{1}{\left(b-c\right)\left(c-a\right)}+\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)
b) \(\dfrac{\left[a^2-\left(b+c\right)^2\right]\left(a+b-c\right)}{\left(a+b+c\right)\left(a^2+c^2-2ac-b^2\right)}\)
c) \(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
d) \(\left[\dfrac{x^2-y^2}{xy}-\dfrac{1}{x+y}\left(\dfrac{x^2}{y}-\dfrac{y^2}{x}\right)\right]:\dfrac{x-y}{x}\)
Cho x, y, z là các số thực khác 0 thỏa mãn:
\(x\left(\dfrac{1}{y}+\dfrac{1}{z}\right)+y\left(\dfrac{1}{x}+\dfrac{1}{z}\right)+z\left(\dfrac{1}{x}+\dfrac{1}{y}\right)=-2\) và x3 + y3 + z3 =1
Tính giá trị của biểu thức P= \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\)
Thực hiện các phép tính với các phân thức sau:
a) \(\dfrac{4a^2-3a+5}{a^3-1}-\dfrac{1-2a}{a^2+a+1}-\dfrac{6}{a-1}\)
b) \(\dfrac{5}{a+1}-\dfrac{10}{a-\left(a^2+1\right)}-\dfrac{15}{a^3+1}\)
c) \(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)
d) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\)
e) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
f) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
1.Cho x+y=7 và x.y=12. Tính giá trị của A=\(x^4+y^4\).
2.Cho ba số a,b,c khác 0 và a+b+c=0. Tính A=\(\dfrac{a^2}{bc}+\dfrac{b^2}{ac}+\dfrac{c^2}{ba}\)
3.Cho x=y+1. Chứng tỏ rằng \(\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)=x^8-y^8\)
Rút gọn các biểu thức:
a) {\(\dfrac{1}{x^2}\) + \(\dfrac{1}{y^2}\) + \(\dfrac{2}{x+y}\)(\(\dfrac{1}{x}\) + \(\dfrac{1}{y}\))} : \(\dfrac{x^3+y^3}{x^2y^2}\)
b) {\(\dfrac{1}{\left(2x-y\right)^2}\) + \(\dfrac{2}{4x^2-y^2}\) + \(\dfrac{1}{\left(2x+y\right)^2}\)} . \(\dfrac{4x^2+4xy+y^2}{16x}\)
c) (\(\dfrac{x^2-xy}{x^2y+y^3}\) - \(\dfrac{2x^2}{y^3-xy^2+x^2y-x^3}\))(1 - \(\dfrac{y-1}{x}\) - \(\dfrac{y}{x^2}\))
1. Thực hiện phép tính
\(A=\dfrac{x^3}{x+2018}.\dfrac{2x+1954}{x+1}+\dfrac{x^3}{x+2018}.\dfrac{21-x}{x+1}\)
\(E=\left(\dfrac{1}{\left(2x-y\right)^2}+\dfrac{2}{4x^2-y^2}+\dfrac{1}{\left(2x+y\right)^2}\right).\dfrac{4x^2+4xy+y^2}{16x}\)
\(B=\dfrac{x^2+2x+4}{x^2-2}\)
2. Cho \(M=\dfrac{12}{x^2-4x+6}\) . Tìm Max của M.
Éc, giải hộ tui đi.
