\(\sum\limits^{2016}_{x=1}\left(\dfrac{x^2}{\left(2x-1\right)\left(2x+1\right)}\right)\)
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Bình luận (3)
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Các câu hỏi tương tự
Tính các tổng sau :
a, \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+......+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\)
b, \(\dfrac{1}{1.5}+\dfrac{1}{5.9}+\dfrac{1}{9.11}+........+\dfrac{1}{\left(4n-3\right)\left(4n+1\right)}\)
c,\(\dfrac{7}{1.8}+\dfrac{7}{8.15}+\dfrac{7}{15.22}+....+\dfrac{1}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\)
Thực hiện phép tính:
a) \(\dfrac{x^2}{x-1}+\dfrac{1-2x}{x-1}\)
b) \(\dfrac{x}{x-3}+\dfrac{-9}{x^2-3x}\)
c) \(\dfrac{3}{x-3}-\dfrac{6x}{9-x^2}+\dfrac{x}{x+3}\)
d) \(\dfrac{5x+10}{4x-8}.\dfrac{x-2}{x+2}\)
e) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^2}\)
a) dfrac{2a-1}{2a+1}-dfrac{2a-3}{2a-1}
b) dfrac{1}{x+1}-dfrac{1}{x-1}-dfrac{2x^2}{1-x^2}
c) dfrac{x+1}{left(x+2right)^2}-dfrac{1}{x+2}-dfrac{1}{1-x^2}
d) dfrac{x-5}{x^2+3x}+dfrac{6}{x+3}
e) x+2+dfrac{3}{x-2}
g) dfrac{4-x}{x^2-4x}+dfrac{3}{x}+dfrac{-2}{x+1}
h) dfrac{x+1}{x-3}+dfrac{-2x^2+2x}{x^2-9}+dfrac{x-1}{x+3}
i) dfrac{x}{x^2-4x}-dfrac{3}{5x}
k) dfrac{1}{xy-x^2}-dfrac{1}{y^2-xy}
Đọc tiếp
a) \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)
b) \(\dfrac{1}{x+1}-\dfrac{1}{x-1}-\dfrac{2x^2}{1-x^2}\)
c) \(\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}-\dfrac{1}{1-x^2}\)
d) \(\dfrac{x-5}{x^2+3x}+\dfrac{6}{x+3}\)
e) \(x+2+\dfrac{3}{x-2}\)
g) \(\dfrac{4-x}{x^2-4x}+\dfrac{3}{x}+\dfrac{-2}{x+1}\)
h) \(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
i) \(\dfrac{x}{x^2-4x}-\dfrac{3}{5x}\)
k) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
Bài 1:i)dfrac{x+1}{x-5}+dfrac{x-18}{x-5}-dfrac{x+2}{5-x}j)dfrac{3xleft(x-2right)}{3x-2}+dfrac{6x^2}{3x-2}-dfrac{2left(2-3xright)}{2-3x}n)dfrac{2}{x}+dfrac{3}{x-1}+dfrac{1-4x}{x^2-x}Bài 2:j)dfrac{2}{3x}-dfrac{1}{2x-2}-dfrac{x-4}{6x-6x^2}
Đọc tiếp
Bài 1:
i)\(\dfrac{x+1}{x-5}\)+\(\dfrac{x-18}{x-5}\)-\(\dfrac{x+2}{5-x}\)
j)\(\dfrac{3x\left(x-2\right)}{3x-2}\)+\(\dfrac{6x^2}{3x-2}\)-\(\dfrac{2\left(2-3x\right)}{2-3x}\)
n)\(\dfrac{2}{x}\)+\(\dfrac{3}{x-1}\)+\(\dfrac{1-4x}{x^2-x}\)
Bài 2:
j)\(\dfrac{2}{3x}\)-\(\dfrac{1}{2x-2}\)-\(\dfrac{x-4}{6x-6x^2}\)
a) dfrac{4x}{x^2+2x}+dfrac{8}{x^2+2x} b) dfrac{2x-3x}{x-2}-dfrac{2x-4}{x-2} c) dfrac{2x-1}{x+3}-dfrac{3x+2}{x+3}d) dfrac{11x}{2x-3}-dfrac{18-x}{2x-3}e) dfrac{3left(x-2right)}{2x+1}-dfrac{9x-3}{2x+1}
Đọc tiếp
a) \(\dfrac{4x}{x^2+2x}\)+\(\dfrac{8}{x^2+2x}\)
b) \(\dfrac{2x-3x}{x-2}\)-\(\dfrac{2x-4}{x-2}\)
c) \(\dfrac{2x-1}{x+3}\)-\(\dfrac{3x+2}{x+3}\)
d) \(\dfrac{11x}{2x-3}\)-\(\dfrac{18-x}{2x-3}\)
e) \(\dfrac{3\left(x-2\right)}{2x+1}\)-\(\dfrac{9x-3}{2x+1}\)
Giải các phương trình sau :
1.dfrac{14}{3x-12}-dfrac{2+x}{x-4}dfrac{3}{8-2x}-dfrac{5}{6}
2.dfrac{12}{1-9x^2}dfrac{1-3x}{1+3x}-dfrac{1+3x}{1-3x}
3.dfrac{x+5}{x^2-5x}-dfrac{x+25}{2x^2-50}dfrac{x-5}{2x^2+10x}
4.dfrac{6x_{ }+1}{x^2-7x+10}+dfrac{5}{x-2}dfrac{3}{x-5}
5.dfrac{2}{x^2-4}-dfrac{x-1}{xleft(x-2right)}+dfrac{x-4}{xleft(x+2right)}0
6.dfrac{2}{x+2}-dfrac{2x^2+16}{x^3+8}dfrac{5}{x^2-2x+4}
Đọc tiếp
Giải các phương trình sau :
1.\(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
2.\(\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
3.\(\dfrac{x+5}{x^2-5x}-\dfrac{x+25}{2x^2-50}=\dfrac{x-5}{2x^2+10x}\)
4.\(\dfrac{6x_{ }+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
5.\(\dfrac{2}{x^2-4}-\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x-4}{x\left(x+2\right)}=0\)
6.\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
Cho các số a,b,c khác 0. Tính giá trị của biểu thức:
T=\(x^{2016}+y^{2016}+z^{2016}\) biết x,y,z thõa mãn \(\dfrac{x^2+y^2+z^2}{a^2+b^2+c^2}=\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}\)
Thực hiện phép tính:
1. \(\dfrac{x}{x+1}-\dfrac{2x}{x-1}+\dfrac{x+3}{x^2-1}\)
2. \(\dfrac{5}{x+1}-\dfrac{10}{x-x^2-1}-\dfrac{15}{x^3+1}\)
3. \(\dfrac{2}{2x+1}-\dfrac{1}{2x-1}-\dfrac{2}{1-4x^2}\)
4. \(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\)
Tính
a)left(dfrac{left(x-1right)^2}{left(3x+x-1right)^2}-dfrac{1-2x^2+4x}{x^3-1}+dfrac{1}{x-1}right):dfrac{x^2+x}{x^2+1}
b)left(dfrac{3left(x+2right)}{2left(x^3+x^2+x+1right)}+dfrac{2x^2-x+10}{2left(x^3+x^2+x+1right)}right):left(dfrac{5}{x^2+1}+dfrac{3}{2left(x+1right)}-dfrac{3}{2left(x-1right)}right).dfrac{2}{x-1}
c)left(dfrac{x^2}{x^2-5x+6}+dfrac{x^2}{x^2-3x+2}right):dfrac{left(x-1right)left(x-3right)}{x^4+x^2+1}
Đọc tiếp
Tính
a)\(\left(\dfrac{\left(x-1\right)^2}{\left(3x+x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right):\dfrac{x^2+x}{x^2+1}\)
b)\(\left(\dfrac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\dfrac{2x^2-x+10}{2\left(x^3+x^2+x+1\right)}\right):\left(\dfrac{5}{x^2+1}+\dfrac{3}{2\left(x+1\right)}-\dfrac{3}{2\left(x-1\right)}\right).\dfrac{2}{x-1}\)
c)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)