Toán Lớp 8: giải các phương trình sau
c, x+1/x-1 – x-1/x+1=4/x^2-1
d, 2x- 2x^2/x+3= 4x/x+3 + 2/7
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Toán Lớp 8: giải các phương trình sau
c, x+1/x-1 – x-1/x+1=4/x^2-1
d, 2x- 2x^2/x+3= 4x/x+3 + 2/7
Comments ( 2 )
c)Dkxd:x\# 1;x\# – 1\\
\dfrac{{x + 1}}{{x – 1}} – \dfrac{{x – 1}}{{x + 1}} = \dfrac{4}{{{x^2} – 1}}\\
\Leftrightarrow \dfrac{{{{\left( {x + 1} \right)}^2} – {{\left( {x – 1} \right)}^2}}}{{\left( {x + 1} \right)\left( {x – 1} \right)}} = \dfrac{4}{{\left( {x – 1} \right)\left( {x + 1} \right)}}\\
\Leftrightarrow {x^2} + 2x + 1 – {x^2} + 2x – 1 = 4\\
\Leftrightarrow 4x = 4\\
\Leftrightarrow x = 1\left( {ktm} \right)
\end{array}$
d)Dkxd:x\# – 3\\
2x – \dfrac{{2{x^2}}}{{x + 3}} = \dfrac{{4x}}{{x + 3}} + \dfrac{2}{7}\\
\Leftrightarrow \dfrac{{7\left( {x + 3} \right).2x – 2{x^2}.7}}{{7\left( {x + 3} \right)}} = \dfrac{{4x.7 + 2.\left( {x + 3} \right)}}{{7\left( {x + 3} \right)}}\\
\Leftrightarrow 14{x^2} + 42x – 14{x^2} = 28x + 2x + 6\\
\Leftrightarrow 12x = 6\\
\Leftrightarrow x = \dfrac{1}{2}\left( {tmdk} \right)\\
Vay\,x = \dfrac{1}{2}
\end{array}$