Toán Lớp 8: x+1/x-1 – x-1/ x+1= 2x – 1/ 2x + 4x + 1 / 2x =
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Toán Lớp 8: x+1/x-1 – x-1/ x+1= 2x – 1/ 2x + 4x + 1 / 2x =
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+ )\dfrac{{x + 1}}{{x – 1}} – \dfrac{{x – 1}}{{x + 1}}\\
= \dfrac{{\left( {x + 1} \right).\left( {x + 1} \right) – \left( {x – 1} \right).\left( {x – 1} \right)}}{{\left( {x – 1} \right).\left( {x + 1} \right)}}\\
= \dfrac{{{{\left( {x + 1} \right)}^2} – {{\left( {x – 1} \right)}^2}}}{{{x^2} – 1}}\\
= \dfrac{{{x^2} + 2x + 1 – {x^2} + 2x – 1}}{{{x^2} – 1}}\\
= \dfrac{{4x}}{{{x^2} – 1}}\\
+ )\dfrac{{2x – 1}}{{2x}} + \dfrac{{4x + 1}}{{2x}}\\
= \dfrac{{2x – 1 + 4x + 1}}{{2x}}\\
= \dfrac{{6x}}{{2x}}\\
= 3
\end{array}$