Toán Lớp 8: Tính
a, x^2/x-2 + 3x/x-2 – x-4/x-2
b, 2/x^2-1 + x+1/x-1 – x-1/x+1
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Toán Lớp 8: Tính
a, x^2/x-2 + 3x/x-2 – x-4/x-2
b, 2/x^2-1 + x+1/x-1 – x-1/x+1
Comments ( 1 )
a)\dfrac{{{x^2} + 2x + 4}}{{x – 2}}\\
b)\dfrac{{4x + 2}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}
\end{array}\)
a)\dfrac{{{x^2}}}{{x – 2}} + \dfrac{{3x}}{{x – 2}} – \dfrac{{x – 4}}{{x – 2}}\\
= \dfrac{{{x^2} + 3x – x + 4}}{{x – 2}}\\
= \dfrac{{{x^2} + 2x + 4}}{{x – 2}}\\
b)\dfrac{2}{{{x^2} – 1}} + \dfrac{{x + 1}}{{x – 1}} – \dfrac{{x – 1}}{{x + 1}}\\
= \dfrac{{2 + {{\left( {x + 1} \right)}^2} – {{\left( {x – 1} \right)}^2}}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{2 + {x^2} + 2x + 1 – {x^2} + 2x – 1}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{4x + 2}}{{\left( {x – 1} \right)\left( {x + 1} \right)}}
\end{array}\)