rút gọn B = ( 1 - 1/2 ) x ( 1 -1/3 ) x ( 1 - 1/4 ) .... ( 1 -1/20 )
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Rút gọn
a) (x^2-1)^3 - (x^4+x^2+1) ).(x^2-1)
b) (x^4 - 3x^2+9).(x^2+3) - (3+x^2)^3
Rút gọn B = (2x+3)\(^2\)-(4x+6)(x+1)+(x+1)\(^2\)
Rút gọn biểu thức
Rút gọn biểu thức
(x-1)(x-2)(x+2)-(x-3)^3
(xy-1)(xy-2)-(xy-2)^2
(x-1)(x-2)(x+2)-(x-3)\(^3\)
=(x-1)(x\(^2\)-4)-(x-3)\(^3\)
(xy-1)(xy-2)-(xy-2)\(^2\)
=(xy-2)(xy-1-xy+2)
=xy-2
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Rút gọn biểu thức:
a) \(\dfrac{3x+21}{x^2-9}+\dfrac{2}{x+3}-\dfrac{3}{x-3}\)
b) \(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\)
\(a,\dfrac{3x+21}{x^2-9}+\dfrac{2}{x+3}-\dfrac{3}{x-3}\\ =\dfrac{3x+21}{\left(x-3\right)\left(x+3\right)}+\dfrac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{3x+21}{\left(x-3\right)\left(x+3\right)}+\dfrac{2x-6}{\left(x-3\right)\left(x+3\right)}-\dfrac{3x+9}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{3x+21+2x-6-3x-9}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{2x+6}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{2}{x-3}\)
\(b,\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\\ =\dfrac{\left(3x+1\right)\left(x+1\right)}{\left(x-1\right)^2\left(x+1\right)}-\dfrac{\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)}-\dfrac{x+3}{x^2-1}\\ =\dfrac{3x^2+4x+1}{\left(x-1\right)^2\left(x+1\right)}-\dfrac{x^2-2x+1}{\left(x-1\right)^2\left(x+1\right)}-\dfrac{\left(x+3\right)\left(x-1\right)}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{3x^2+4x+1-x^2+2x-1}{\left(x-1\right)^2\left(x+1\right)}-\dfrac{x^2+2x-3}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{2x^2+6x-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{x^2+4x+3}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{\left(x^2+3x\right)+\left(x+3\right)}{\left(x-1\right)^2\left(x+1\right)}\)
\(=\dfrac{x\left(x+3\right)+\left(x+3\right)}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{x+3}{\left(x-1\right)^2}\)
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cho bt: 1/x - 1 + 1/ x+ 1 + 4x +2/ x2 - 1
a, rút gọn bt.
b, tìm x khi A = 4/2015
rút gọn -|x 1/2| |1/3-x| khi x>2
Rút gọn
\(\dfrac{x^3-3x^2+3x-1}{x^2y-xy-x+1}\)
\(=\dfrac{\left(x-1\right)^3}{xy\left(x-1\right)-\left(x-1\right)}=\dfrac{\left(x-1\right)^3}{\left(xy-1\right)\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{xy-1}\left(xy\ne1;x\ne1\right)\)
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Rút gọn biểu thức M = \(\dfrac{1}{x^2-3x+2}+\dfrac{1}{x^2-5x+6}+\dfrac{1}{x^2-7x+12}+\dfrac{1}{x^2-9x+20}\)
\(M=\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-4\right)\left(x-5\right)}\)
\(M=\dfrac{1}{x-1}-\dfrac{1}{x-2}+\dfrac{1}{x-2}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-4}+\dfrac{1}{x-4}-\dfrac{1}{x-5}\)
\(M=\dfrac{1}{x-1}-\dfrac{1}{x-5}\)
\(M=\dfrac{x-5-x+1}{\left(x-5\right)\left(x-1\right)}=-\dfrac{4}{x^2-6x+5}\)
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B= \(\frac{1}{x-1}-\frac{x^3-x}{x^2+1}.\left(\frac{1}{1-2x+x^2}+\frac{1}{1-x^2}\right)\)
Tìm Tập xác định
Rút gọn B
ĐK: x khác 1 ; -1
\(B=\frac{1}{x-1}-\frac{x^3-x}{x^2+1}.\left(\frac{1}{1-2x+x^2}+\frac{1}{1-x^2}\right)\)
\(=\frac{1}{x-1}-\frac{x^3-x}{x^2+1}.\left(\frac{1+x}{\left(1-x\right)^2\left(1+x\right)}+\frac{1-x}{\left(1-x\right)^2\left(1+x\right)}\right)\)
=\(\frac{1}{x-1}-\frac{x\left(x-1\right)\left(x+1\right)}{x^2+1}.\frac{2}{\left(1-x\right)^2\left(1+x\right)}=\frac{1}{x-1}-\frac{2x}{\left(x^2+1\right)\left(1-x\right)}\)
\(=\frac{x^2+1}{\left(x^2+1\right)\left(x-1\right)}+\frac{2x}{\left(x^2+1\right)\left(x-1\right)}=\frac{x^2+2x+1}{\left(x^2+1\right)\left(x-1\right)}=\)
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