Question

rút gọn biểu thức a=(x/x-2-2/x+2):x^2+4/x+2

Answer 1

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

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

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

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

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

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

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

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

Answer 2

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Answer 3

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

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

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

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

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

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