Toán Lớp 8: kết quả của phép tính x/x+1 – x-1/x^2 -1
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Toán Lớp 8: kết quả của phép tính x/x+1 – x-1/x^2 -1
Comments ( 2 )
#andy
\[\begin{array}{l}
\dfrac{x}{{x + 1}} – \dfrac{{x – 1}}{{{x^2} – 1}}\\
= \dfrac{x}{{x + 1}} – \dfrac{{x – 1}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
DKXD:\left\{ \begin{array}{l}
x – 1 \ne 0\\
x + 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne 1\\
x \ne – 1
\end{array} \right.\\
\dfrac{x}{{x + 1}} – \dfrac{{x – 1}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{x\left( {x – 1} \right)}}{{\left( {x + 1} \right)\left( {x – 1} \right)}} – \dfrac{{x – 1}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{{x^2} – x – x + 1}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – 2x + 1}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{{\left( {x – 1} \right)}^2}}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{x – 1}}{{x + 1}}
\end{array}\]
Answer
x/{x + 1} – {x – 1}/{x^2 – 1} (ĐK : x \ne +-1)
= x/{x + 1} – {x – 1}/{x^2 – 1^2}
= x/{x + 1} – {x – 1}/{(x – 1) . (x + 1)}
= {x . (x – 1)}/{(x – 1) . (x + 1)} – {x – 1}/{(x – 1) . (x + 1)}
= {x^2 – x}/{(x – 1) . (x + 1)} – {x – 1}/{(x – 1) . (x + 1)}
= {(x^2 – x) – (x – 1)}/{(x – 1) . (x + 1)}
= {x^2 – x – x + 1}/{(x – 1) . (x + 1)}
= {x^2 – 2x + 1}/{(x – 1) . (x + 1)}
= {x^2 – 2 . x . 1 + 1^2}/{(x – 1) . (x + 1)}
= {(x – 1)^2}/{(x – 1) . (x + 1)}
= {x – 1}/{x + 1}