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Zi Heo
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nthv_.
30 tháng 10 2021 lúc 16:58

a. \(\dfrac{\left(x-2\right)^2}{2x\left(x-2\right)}=\dfrac{x-2}{2x}\)

b. \(\dfrac{\dfrac{1}{2}-2}{2.\dfrac{1}{2}}=-1,5\)

Duong Thi Nhuong
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Persistent
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Duong Thi Nhuong
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Mỹ Duyên
27 tháng 5 2017 lúc 11:42

Haizzzzzzzzzzz! huhu

ĐKXĐ: \(x\ne0;\dfrac{-1}{2};\dfrac{1}{2}\)

\(\left(\dfrac{1+x}{x}+\dfrac{1}{4x^2}\right)\left(\dfrac{1-2x}{1+2x}-\dfrac{1}{1-4x^2}.\dfrac{1-4x+4x^2}{1+2x}\right)-\dfrac{1}{2x}\)

=

\(\dfrac{4x\left(x+1\right)+1}{4x^2}.\left[\dfrac{\left(1-2x\right)\left(1+2x\right)}{\left(2x+1\right)^2}-\dfrac{1}{\left(1-2x\right)\left(1+2x\right)}.\dfrac{\left(1-2x\right)^2}{1+2x}\right]\)\(-\dfrac{1}{2x}\)

= \(\dfrac{\left(2x+1\right)^2}{4x^2}.\left(\dfrac{1-4x^2}{\left(2x+1\right)^2}-\dfrac{1-2x}{\left(2x+1\right)^2}\right)-\dfrac{1}{2x}\)

= \(\dfrac{\left(2x+1\right)^2}{4x^2}.\dfrac{2x\left(1-2x\right)}{\left(2x+1\right)^2}-\dfrac{1}{2x}\)

= \(\dfrac{1-2x}{2x}-\dfrac{1}{2x}=\dfrac{-2x}{2x}=1\)

Duong Thi Nhuong
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Nguyễn Lê Phước Thịnh
2 tháng 2 2022 lúc 23:31

\(=\dfrac{4x\left(x+1\right)+1}{4x^2}\cdot\left(\dfrac{-\left(2x-1\right)}{2x+1}+\dfrac{1}{\left(2x+1\right)\left(2x-1\right)}\cdot\dfrac{\left(2x-1\right)^2}{2x+1}\right)-\dfrac{1}{2x}\)

\(=\dfrac{\left(2x+1\right)^2}{4x^2}\cdot\left(\dfrac{-\left(2x-1\right)}{2x+1}+\dfrac{2x-1}{\left(2x+1\right)^2}\right)-\dfrac{1}{2x}\)

\(=\dfrac{\left(2x+1\right)^2}{4x^2}\cdot\dfrac{-\left(2x-1\right)\left(2x+1\right)+2x-1}{\left(2x+1\right)^2}-\dfrac{1}{2x}\)

\(=\dfrac{-4x^2+1+2x-1}{4x^2}-\dfrac{1}{2x}\)

\(=\dfrac{-4x^2+2x}{4x^2}-\dfrac{1}{2x}\)

\(=\dfrac{-2x\left(2x-1\right)}{2x\cdot2x}-\dfrac{1}{2x}\)

\(=\dfrac{-2x+1-1}{2x}=\dfrac{-2x}{2x}=-1\)

Duong Thi Nhuong
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Nguyễn Lê Phước Thịnh
31 tháng 1 2022 lúc 20:54

\(A=\left(\dfrac{x^2-2x+1}{x^2+x+1}-\dfrac{-2x^2+4x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x-1}\right):\dfrac{2x}{x^3+x}\)

\(=\dfrac{x^3-3x^2+3x-1+2x^2-4x-1+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\)

\(=\dfrac{x^3-1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}=\dfrac{x^2+1}{2}\)

Vân Lưu
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Nguyễn Lê Phước Thịnh
13 tháng 5 2022 lúc 23:53

\(Q=\left(\dfrac{2x-x^2}{2x^2}+\dfrac{8-2x^2}{\left(x-2\right)\left(x^2+4\right)}\right)\cdot\left(\dfrac{2}{x^2}+\dfrac{1-x}{x}\right)\)

\(=\left(\dfrac{2-x}{2x}-\dfrac{2\left(x+2\right)}{x^2+4}\right)\cdot\dfrac{2+x-x^2}{x^2}\)

\(=\dfrac{2x^2+8-x^3-4x-4x\left(x+2\right)}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{2x^2+8-x^3-4x-4x^2-8x}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{-x^3-2x^2-12x+8}{2x\left(x^2+4\right)}\cdot\dfrac{-\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{\left(x^3+2x^2+12x-8\right)\left(x-2\right)\left(x+1\right)}{2x^3\left(x^2+4\right)}\)

Zi Heo
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Nguyễn Lê Phước Thịnh
15 tháng 10 2021 lúc 23:35

a: \(\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\)

b: \(\dfrac{x^2-4xy+4y^2-4}{2x^2-4xy+4x}\)

\(=\dfrac{\left(x-2y\right)^2-4}{2x\left(x-2y+2\right)}\)

\(=\dfrac{x-2y-2}{2x}\)

Trần Đăng Khoa
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