Toán Lớp 8: 3) x + x-1/x-2 = 3 + 1/x-2
5) x-1/x+3 – x/x-3 = 7x-3/9-x^2
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Toán Lớp 8: 3) x + x-1/x-2 = 3 + 1/x-2
5) x-1/x+3 – x/x-3 = 7x-3/9-x^2
Comments ( 2 )
3)\\
x + \frac{{x – 1}}{{x – 2}} = 3 + \frac{1}{{x – 2}}\,\,\,DKXD:x \ne 2\\
\Rightarrow x\left( {x – 2} \right) + \left( {x – 1} \right) = 3\left( {x – 2} \right) + 1\\
\Rightarrow {x^2} – 2x + x – 1 = 3x – 6 + 1\\
\Rightarrow {x^2} – x – 1 – 3x + 6 – 1 = 0\\
\Rightarrow {x^2} – 4x + 4 = 0\\
\Rightarrow {\left( {x – 2} \right)^2} = 0\\
\Rightarrow x = 2\left( {khong\,\,nhan} \right)\\
5)\\
\frac{{x + 1}}{{x + 3}} – \frac{x}{{x – 3}} = \frac{{7x – 3}}{{9 – {x^2}}}\,\,DKXD:\,x \ne 3; – 3\\
\Rightarrow \left( {x – 1} \right)\left( {x – 3} \right) – x\left( {x + 3} \right) = – 7x + 3\\
\Rightarrow {x^2} – 3x – x + 3 – {x^2} – 3x + 7x – 3 = 0\\
\Rightarrow 0 = 0\\
\Rightarrow vo\,\,so\,\,nghiem\\
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