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NC
1
29 tháng 9 2019
\(A=\frac{4x}{x^2-2x}+\frac{3}{2-x}+\frac{12x}{x^3-4x}\)
\(A=\frac{4x}{x\left(x-2\right)}-\frac{3}{x-2}+\frac{12x}{x\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{4x\left(x+2\right)-3x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{x^2+2x+12x}{x\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{x^2+14x}{x\left(x-2\right)\left(x+2\right)}\)
TA
rút gọn biểu thức A =\(\left(\frac{4x}{x^2-4}+\frac{2x-4}{x+2}\right).\frac{x+2}{2x}+\frac{2}{2-x}\)
0
19 tháng 3 2020
=[x(x-2)/2(x2+4)-2x2/(4+x2)(2-x)][x(x-2)(x+1)/x3]
={[x(x-2)(2-x)-4x2 ]/2(2-x)(4+x2)} .[x(x-2)(x+1)/x3 ]
=[-x(x2+4)/2(2-x)(4+x2)].[x(x-2)(x+1)/x3 ]
=-x.x(x-2)(x+1)/2(2-x)x3
=(x+1)/2x
6 tháng 1 2018
\(P=\frac{2x^5-x^4-2x+1}{4x^2-1}+\frac{8x^2-4x+2}{ }\)
\(P=\frac{x^4\left(2x-1\right)-\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}+\frac{2\left(4x^2-2x+1\right)}{\left(2x+1\right)\left(4x^2-2x+1\right)}\)
\(P=\frac{\left(x^4-1\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}+\frac{2}{2x+1}\)
\(P=\frac{x^4-1}{2x+1}+\frac{2}{2x+1}\)
\(P=\frac{x^4+1}{2x+1}\)
Vậy \(P=\frac{x^4+1}{2x+1}\)
N
11 tháng 12 2018
a)\(\frac{x^3-x}{3x+3}=\frac{x.\left(x^2-1\right)}{3.\left(x+1\right)}=\frac{x.\left(x-1\right).\left(x+1\right)}{3.\left(x+1\right)}=\frac{x.\left(x+1\right)}{3}=\frac{x^2+x}{3}\)
\(A=\frac{4x}{x^2+2x}+\frac{3}{2-x}+\frac{12}{x^2-4}\)(ĐK: \(x\ne0,x\ne\pm2\))
\(A=\frac{4}{x+2}+\frac{3}{2-x}+\frac{12}{\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{4.\left(x-2\right)-3\left(x+2\right)+12}{\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{4x-8-3x-6+12}{\left(x-2\right)\left(x+2\right)}\)
\(A=\frac{x-2}{\left(x-2\right)\left(x+2\right)}=\frac{1}{x+2}\)
\(A=\frac{4x}{x^2+2x}+\frac{3}{2-x}+\frac{12}{x^2-4x}\)
\(=\frac{4x}{x\left(x+2\right)}-\frac{3}{x-2}+\frac{12}{x\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x\left(x-2\right)}{x\left(x+2\right)\left(x-2\right)}-\frac{3x\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}+\frac{12}{x\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x^2-8x-3x^2-6x+12}{x\left(x-2\right)\left(x+2\right)}=\frac{x^2-14x+12}{x\left(x-2\right)\left(x+2\right)}\)