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\(\dfrac{-1}{\left(x-1\right)\left(2x+1\right)}.\dfrac{x-1}{1}=\dfrac{-1}{2x+1}\)
a: \(A=\dfrac{x-1+2x^2+2x+2-x^2-2x}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x-1}\)
\(\left(x-4\right)\left(x-2\right)-\left(x-1\right)\left(x-3\right)\)
\(=x^2-2x-4x+8-\left(x^2-3x-x+3\right)\)
\(=x^2-2x-4x+8-x^2+3x+x-3\)
\(=-2x+5\)
(x - 4).(x - 2) - (x - 1).(x - 3)
= x2 - 2x - 4x + 8 - ( x2 - 3x - x + 3 )
= x2 - 2x - 4x + 8 - x2 + 3x + x - 3
= 5 - 2x
......
\(=\left(x-\dfrac{1}{3}\right)\left(\dfrac{4}{3}x+\dfrac{1}{9}-x+\dfrac{1}{3}\right)\\ =\left(x-\dfrac{1}{3}\right)\left(\dfrac{1}{3}x+\dfrac{4}{9}\right)\\ =\dfrac{1}{3}x^2+\dfrac{4}{9}x-\dfrac{1}{9}x-\dfrac{4}{27}\\ =\dfrac{1}{3}x^2+\dfrac{1}{3}x-\dfrac{4}{27}\)
\(\dfrac{x}{x+1}+1\)
\(=\dfrac{x+x+1}{x+1}\)
\(=\dfrac{2x+1}{x+1}\)
ĐKXĐ : x \(\ne-1\)
\(=\dfrac{x}{x+1}+\dfrac{x+1}{x+1}\)
\(=\dfrac{2x+1}{x+1}\)