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29 tháng 11 2021
\(\dfrac{3-3x}{2x}+\dfrac{3x-1}{2x-1}+\dfrac{11x-5}{2x-4x^2}\\ =\dfrac{\left(3-3x\right)\left(1-2x\right)}{2x\left(1-2x\right)}-\dfrac{2x\left(3x-1\right)}{2x\left(1-2x\right)}+\dfrac{11x-5}{2x\left(1-2x\right)}\\ =\dfrac{3-9x+6x^2}{2x\left(1-2x\right)}-\dfrac{6x^2-2x}{2x\left(1-2x\right)}+\dfrac{11x-5}{2x\left(1-2x\right)}\\ =\dfrac{3-9x+6x^2-6x^2+2x+11x-5}{2x\left(1-2x\right)}\\ =\dfrac{-2}{2x\left(1-2x\right)}\\ =\dfrac{-1}{x\left(1-2x\right)}\)
29 tháng 11 2021
\(\dfrac{x+10}{x-2}+\dfrac{x-18}{x+2}+\dfrac{x+2}{x^2-4}=\dfrac{\left(x+10\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{\left(x-18\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+12x+20+x^2-16x-36+x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2-3x-14}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(2x^2+4x\right)-\left(7x+14\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x\left(x+2\right)-7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(2x-7\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x-7}{x-2}\)
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17 tháng 7 2023
1) \(x\left(4x+1\right)\)
2) \(3\left(x-3y\right)\)
3) \(\left(2x+1\right)\left(2x+1+2\right)=\left(2x+1\right)\left(2x+3\right)\)
18 tháng 12 2021
a: \(=\dfrac{4x-2+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2x-1}{2x\left(2x-1\right)}\)
\(\dfrac{1-2x}{2x}+\dfrac{2x}{2x-1}+\dfrac{1}{2x-4x^2}=\dfrac{1-2x}{2x}-\dfrac{2x}{1-2x}+\dfrac{1}{2x\left(1-2x\right)}=\dfrac{\left(1-2x\right)^2}{2x\left(1-2x\right)}-\dfrac{2x.2x}{2x\left(1-2x\right)}+\dfrac{1}{2x\left(1-2x\right)}=\dfrac{1-4x+4x^2-4x^2+1}{2x\left(1-2x\right)}=\dfrac{2-4x}{2x\left(1-2x\right)}=\dfrac{2\left(1-2x\right)}{2x\left(1-2x\right)}=\dfrac{1}{x}\)
\(=\dfrac{\left(2x-1\right)\left(1-2x\right)}{2x\left(2x-1\right)}+\dfrac{4x^2}{2x\left(2x-1\right)}+\dfrac{-1}{2x\left(2x-1\right)}=\dfrac{\left(2x-1\right)\left(1-2x\right)+4x^2-1}{2x\left(2x-1\right)}=\dfrac{2x-4x^2-1+2x+4x^2-1}{2x\left(2x-1\right)}=\dfrac{4x-2}{2\left(2x-1\right)}=\dfrac{2\left(2x-1\right)}{2\left(2x-1\right)}=\dfrac{2}{2}=1\)