Cho P=\(\frac{x}{x-1}+\frac{3}{x+1}-\frac{6x-4}{x^2-1}\)Rút gọn P
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7 tháng 12 2014
1/(x^2+6x+9)-1/(x^2-6x+9)=(x-3)/(x-3)(x+3)-(x+3)/(x-3)(x+3)= -6/(x-3)(x+3)
1/(x+3)+1/(x-3)=
27 tháng 6 2016
\(=3x^3-\frac{3}{2}x^2-x^3-\frac{1}{2}x+\frac{1}{2}x+2\)
\(=2x^3-\frac{3}{2}x^2+2\)
NT
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NT
1
4 tháng 12 2018
\(\frac{x^4+6x^3+9x^2-1}{x^4+6x^3+7x^2-6x+1}=\frac{\left(x^2\right)^2+2.x^2.3x+\left(3x\right)^2-1}{\left(x^2\right)^2+2.x^2.3x+\left(3x\right)^2-2x^2-6x+1}\)
\(=\frac{\left(x^2+3x\right)^2-1}{\left(x^2+3x\right)^2-2\left(x^2+3x\right)+1}\)
\(=\frac{\left(x^2+3x-1\right)\left(x^2+3x+1\right)}{\left(x^2+3x-1\right)^2}=\frac{x^2+3x+1}{x^2+3x-1}\)
26 tháng 6 2017
a)\(Q=\left(\frac{1}{x+1}+\frac{6x+3}{x^3+1}-\frac{2}{x^2-x+1}\right):\left(x+2\right)\)\(\left(ĐKXĐ:x\ne-1\right)\)
\(Q=\left(\frac{x^2-x+1}{x^3+1}+\frac{6x+3}{x^3+1}-\frac{2\left(x+1\right)}{x^3+1}\right):\left(x+2\right)\)
\(Q=\left(x^2-x+1+6x+3-2x-2\right):\left(x+2\right)\)
\(Q=\left(x^2+3x+2\right):\left(x+2\right)\)
\(Q=\left(x+1\right)\left(x+2\right):\left(x+2\right)\)
\(Q=x+1\)
b)Tại \(Q=\frac{1}{3}\)ta được:\(\frac{1}{3}=x+1\)
\(\Rightarrow x=-\frac{2}{3}\)
DT
1
H
1 tháng 12 2018
\(C=\frac{1}{x^2+6x+9}+\frac{1}{6x-x^2-9}+\frac{x}{x^2-9}.\)
\(C=\frac{1}{\left(x+3\right)^2}+\frac{-1}{-\left(6x-x^2-9\right)}+\frac{x}{\left(x+3\right)\left(x-3\right)}\)
\(C=\frac{1}{\left(x+3\right)^2}+\frac{-1}{-6x+x^2+9}+\frac{x}{\left(x+3\right)\left(x-3\right)}\)
\(C=\frac{x-3}{\left(x+3\right)\left(x-3\right)}+\frac{-\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{x}{\left(x+3\right)\left(x-3\right)}\)
\(C=\frac{x-3.-x-3.x}{\left(x+3\right).\left(x-3\right)}=\frac{-6x}{\left(x+3\right)\left(x-3\right)}=\frac{-6x}{\left(x^2-9\right)}\)
\(ĐK:x\ne\pm1\)
\(P=\frac{x}{x-1}+\frac{3}{x+1}-\frac{6x-4}{x^2-1}=\frac{x^2+x}{\left(x-1\right)\left(x+1\right)}+\frac{3x-3}{\left(x+1\right)\left(x-1\right)}-\frac{6x-4}{x^2-1}=\frac{x^2+x}{x^2-1}+\frac{3x-3}{x^2-1}-\frac{6x-4}{x^2-1}=\frac{x^2+4x-6x+1}{x^2-1}=\frac{x^2-2x+1}{x^2-1}=\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\frac{x-1}{x+1}\)
P= (x2-2x+1)/(x2-1)= (x-1)/(x+1)