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ĐKXĐ : \(x\ne\pm\frac{1}{2}\)
\(E=\left(\frac{\left(4x^2+2x\right)\left(1+4x^2\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}-\frac{\left(4x^2-2x\right)\left(1-4x^2\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}\right):\left(\frac{\left(1+2x\right)\left(1+2x\right)}{\left(1-2x\right)\left(1+2x\right)}-\frac{\left(1-2x\right)\left(1-2x\right)}{\left(1+2x\right)\left(1-2x\right)}\right)\)
\(E=\left(\frac{16x^4+8x^3+4x^2+2x+16x^4-8x^3-4x^2+2x}{1-16x^4}\right):\left(\frac{1+2x+x^2-1+2x-x^2}{1-4x^2}\right)\)
\(E=\frac{32x^4+4x}{1-16x^4}:\frac{4x}{1-4x^2}\)
\(E=\frac{4x\left(8x^3+1\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}.\frac{1-4x^2}{4x}\)
\(E=\frac{8x^3+1}{1+4x^2}\)
Study well
E=\(\left(\frac{4x^2+2x}{1-4x^2}-\frac{4x^2-2x}{1+4x^2}\right):\left(\frac{1+2x}{1-2x}-\frac{1-2x}{1+2x}\right)\)
E=\(\left(\frac{\left(4x^2+2x\right)\left(1+4x^2\right)-\left(4x^2-2x\right)\left(1-4x^2\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}\right):\)\(\left(\frac{\left(1+2x\right)^2-\left(1-2x\right)^2}{\left(1-2x\right)\left(1+2x\right)}\right)\)
E=\(\frac{4x^2+16x^4+2x+8x^3-\left(4x^2-16x^4-2x+8x^3\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}:\)\(\left(\frac{\left(1+4x+4x^2\right)-\left(1-4x+4x^2\right)}{\left(1-2x\right)\left(1+2x\right)}\right)\)
E=\(\frac{4x^2+16x^4+2x+8x^3-4x^2+16x^4+2x-8x^3}{\left(1-4x^2\right)\left(1+4x^2\right)}:\)\(\left(\frac{1+4x+4x^2-1+4x-4x^2}{\left(1-2x\right)\left(1+2x\right)}\right)\)
E=\(\frac{16x^4+2x+16x^4+2x}{\left(1-4x^2\right)\left(1+4x^2\right)}:\)\(\left(\frac{8x}{\left(1-2x\right)\left(1+2x\right)}\right)\)
E=\(\frac{32x^4+8x}{\left(1-4x^2\right)\left(1+4x^2\right)}.\frac{1-4x^2}{8x}\)
E=\(\frac{8x\left(4x^3+1\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}.\frac{1-4x^2}{8x}\)
E=\(\frac{4x^3+1}{1+4x^2}\)
E=\(\frac{\left(4x^2+2x\right)\left(1+4x^2\right)-\left(4x^2-2x\right)\left(1-4x^2\right)}{\left(1-4x^2\right)\left(1+4x^2\right)}:\frac{\left(1+2x\right)^2-\left(1-2x\right)^2}{1-4x^2}\)
E=\(\frac{4x^2+16x^4+2x+8x^3-4x^2+16x^2+2x-8x^3}{\left(1-4x^2\right)\left(1+4x^2\right)}.\frac{1-4x^2}{1+4x+4x^2-1+4x-4x^2}\)
E=\(\frac{32x^4+4x}{8x\left(1+4x^2\right)}=\frac{8x^3+1}{2\left(1+4x^2\right)}\)
=[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
a) \(4x^2\left(5x^3-2x+3\right)\)
\(=20x^5-8x^3+12x^2\)
b) \(3y^2\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)\)
\(=12y^5+2y^4-y^2\)
c) \(\left(5x^2-4x\right)\left(x-2\right)\)
\(=5x^3-14x^2+8x\)
d) \(\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)\)
\(=6x^2+22x-55-6x^2-23x-21\)
\(=-x-76\)
1, \(4x^2\left(5x^3-2x+3\right)=20x^5-8x^3+12x^2\)
2, \(3y^2\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)=12y^5+2y^4-y^2\)
3, \(\left(5x^2-4x\right)\left(x-2\right)=5x^3-10x^2-4x^2+8x=5x^3-14x^2+8x\)
4, \(\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)=6x^2+33x-10x-55-\left(6x^2+14x+9x+21\right)\)
\(=6x^2+23x-55-6x^2-23x-21=-76\)
\(A=\left(\frac{3x}{1-2x}-\frac{2x}{1+2x}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\frac{3x+2x}{1-2x}:\frac{2x^2+5}{\left(1-2x\right)^2}\)
\(A=\frac{5x}{1-2x}\cdot\frac{\left(1-2x\right)^2}{2x^2+5}\)
\(A=\frac{5x\left(1-2x\right)\left(1-2x\right)}{\left(1-2x\right)\left(2x^2+5\right)}\)
\(A=\frac{5x\left(1-2x\right)}{2x^2+5}\)
\(A=\frac{5x-10x^2}{2x^2+5}\)
\(A=\left(\frac{3x}{1-2x}-\frac{2x}{1+2x}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\left(\frac{3x.\left(1+2x\right)}{\left(1-2x\right).\left(1+2x\right)}-\frac{2x.\left(1-2x\right)}{\left(1-2x\right).\left(1+2x\right)}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\left(\frac{3x+6x^2}{\left(1-2x\right).\left(1+2x\right)}-\frac{2x-4x^2}{\left(1-2x\right).\left(1+2x\right)}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\left(\frac{3x+6x^2}{\left(1-2x\right).\left(1+2x\right)}+\frac{-\left(2x-4x^2\right)}{\left(1-2x\right).\left(1+2x\right)}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\left(\frac{3x+6x^2-2x+4x^2}{\left(1-2x\right).\left(1+2x\right)}\right):\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\frac{x+10x^2}{\left(1-2x\right).\left(1+2x\right)}:\frac{2x^2+5}{1-4x+4x^2}\)
\(A=\frac{x+10x^2}{\left(1-2x\right).\left(1+2x\right)}:\frac{2x^2+5}{\left(1-2x\right)^2}\)
\(A=\frac{x+10x^2}{\left(1-2x\right).\left(1+2x\right)}.\frac{\left(1-2x\right)^2}{2x^2+5}\)
\(A=\frac{\left(x+10x^2\right).\left(1-2x\right)^2}{\left(1-2x\right).\left(1+2x\right).\left(2x^2+5\right)}\)
\(A=\frac{\left(x+10x^2\right).\left(1-2x\right)}{\left(1+2x\right).\left(2x^2+5\right)}\)
\(A=\frac{x-2x^2+10x^2-20x^3}{2x^2+5+4x^3+10x}\)
\(A=\frac{x+8x^2-20x^3}{2x^2+5+4x^3+10x}\)
Chúc bạn học tốt!