Question

Cho

A=(2x+1/x^2-3x+2)-(x+1/x-1)-(x^2+5/x^2-3x+2)+(x^2+x/x-1)

a. Rút gọn A

b. Tìm x thuộc Z để A thuộc Z

Answer 1

a: \(A=\dfrac{2x+1}{\left(x-1\right)\left(x-2\right)}+\dfrac{x+1}{x-1}-\dfrac{x^2+5}{\left(x-1\right)\left(x-2\right)}+\dfrac{x^2+x}{x-1}\)

\(=\dfrac{2x+1-x^2-5}{\left(x-1\right)\left(x-2\right)}+\dfrac{x+1+x^2+x}{x-1}\)

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

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

\(=\dfrac{x^3-x^2-x-6}{\left(x-1\right)\left(x-2\right)}\)

b: Để A là số nguyên thì \(x^3-3x^2+2x+2x^2-6x+4+3x-10⋮\left(x-1\right)\left(x-2\right)\)

=>\(3x-10⋮x^2-3x+2\)

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