\(=\left(x^3-1\right)\left(x^3+1\right)=x^6-1\)
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Thực hiện phép trừ:
1. 1/x-1 - 1/x+1
2. x/ x^2-1 - 1/x-1
3. 1/y.(x-y) - 1/ x ( x-y )
4. 1/x - 1/ x-1
5. 1/x - 1/ x+1
6. 1/ 2x^2 - 10x - 1/ x-5
7. x-1/x^2 -1 . x+1/x+3
8. 2/ 2x^2 +10x . x+5/3x
Giải pt : a) 2/-x2+6x-8 - x-1/x-2 = x+3/x-4
b) 2/x3-x2-x+1 = 3/1-x2 - 1/x+1
c) x+2/x-2 - 2/x2-2x = 1/x
d) 5/-x2+5x-6 + x+3/2-x = 0
e) x/2x+2 - 2x/x2-2x-3 = x/6-2x
f) 1/x-1 - 3x2/x3-1 = 2x/x2+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)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
Dạng 1: Rút gọn biểu thức
1:3x(x-2)-5x(1-x)-8(x^2-3)
2:(4x-5)(2x+3)-4(x+2)(2x-1)+10x+7
3:(6x+1)^2+(6x-1)^2-2(1+6x)(6x-1)
4: (x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2)
5: (x+1)^3+(x-1)^3+x^3-3x(x+1)(x-1)
6:3(2^2+1)(2^4+1)........(2^64+1)+1
chứng minh rằng :
a) left(dfrac{x^2-2x}{2x^2+8}-dfrac{2x^2}{8-4x+2x^2-x}right)left(1-dfrac{1}{x}-dfrac{2}{x^2}right)dfrac{x+1}{2x}
b)left[dfrac{2}{3x}-dfrac{2}{x+1}left(dfrac{x+1}{3x}-x-1right)right]:dfrac{x+1}{x}dfrac{2x}{x-1}
c)left[dfrac{2}{left(x+1right)^3}left(dfrac{1}{x}+1right)+dfrac{1}{x^2+2x+1}left(dfrac{1}{x^2}+1right)right]:dfrac{x-1}{x^3}dfrac{x}{x-1}
Đọc tiếp
chứng minh rằng :
a) \(\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)=\dfrac{x+1}{2x}\)
b)\(\left[\dfrac{2}{3x}-\dfrac{2}{x+1}\left(\dfrac{x+1}{3x}-x-1\right)\right]:\dfrac{x+1}{x}=\dfrac{2x}{x-1}\)
c)\(\left[\dfrac{2}{\left(x+1\right)^3}\left(\dfrac{1}{x}+1\right)+\dfrac{1}{x^2+2x+1}\left(\dfrac{1}{x^2}+1\right)\right]:\dfrac{x-1}{x^3}=\dfrac{x}{x-1}\)
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. \(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\)
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) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
Rút gọn các biểu thức sau:
a) \(\dfrac{\dfrac{1}{x}+\dfrac{1}{y}}{\dfrac{1}{x}-\dfrac{1}{y}}\)
b) \(\dfrac{\dfrac{x}{x+1}-\dfrac{x-1}{x}}{\dfrac{x}{x-1}-\dfrac{x+1}{x}}\)
c) \(1-\dfrac{x}{1-\dfrac{x}{x+1}}\)
d) \(\dfrac{1-\dfrac{2}{x+1}}{1-\dfrac{x^2-2}{x^2-1}}\)
\(\dfrac{x^2+4x-3}{x^3+1}-\dfrac{x-1}{x^2-x+1}+\dfrac{2}{x+1}\)
(1/x^x+x-2-x/x+1)/(1/x+x-2)