document.write( "Question 119347: Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me.\r
\n" ); document.write( "\n" ); document.write( "x/x-2 - x+1/x = 8/x^2-2x \n" ); document.write( "
Algebra.Com's Answer #87491 by ankor@dixie-net.com(22740)\"\" \"About 
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Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me.
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\n" ); document.write( "The problem as I see it:
\n" ); document.write( "\"x%2F%28%28x-2%29%29\" - \"%28%28x%2B1%29%29%2Fx\" = \"8%2F%28%28x%5E2-2x%29%29\"
\n" ); document.write( "Note that on the last denominator we can factor out x:
\n" ); document.write( "\"x%2F%28%28x-2%29%29\" - \"%28%28x%2B1%29%29%2Fx\" = \"8%2F%28x%28x-2%29%29\"
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\n" ); document.write( "Our common denominator will be x(x-2); Multiple equation by this
\n" ); document.write( "x(x-2)*\"x%2F%28%28x-2%29%29\" - x(x-2)*\"%28%28x%2B1%29%29%2Fx\" = x(x-2)*\"8%2F%28x%28x-2%29%29\"
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\n" ); document.write( "Cancel out the denominators and you have:
\n" ); document.write( "x(x) - (x-2)(x+1) = 8
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\n" ); document.write( "x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)
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\n" ); document.write( "x^2 - x^2 + x + 2 = 8; removed the brackets, changed the signs
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\n" ); document.write( "x = 8 - 2
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\n" ); document.write( "x = 6
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\n" ); document.write( "Check our solution in the original equation:
\n" ); document.write( "\"x%2F%28%28x-2%29%29\" - \"%28%28x%2B1%29%29%2Fx\" = \"8%2F%28%28x%5E2-2x%29%29\"
\n" ); document.write( "Substitute 6 for x
\n" ); document.write( "\"6%2F%28%286-2%29%29\" - \"%28%286%2B1%29%29%2F6\" = \"8%2F%28%286%5E2-2%286%29%29%29\"
\n" ); document.write( "\"6%2F%284%29\" - \"%287%29%2F6\" = \"8%2F%28%2836-12%29%29\"
\n" ); document.write( "Put all fraction over 24:
\n" ); document.write( "\"36%2F%2824%29\" - \"%2828%29%2F24\" = \"8%2F%2824%29%29\"; confirms our solution
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\n" ); document.write( "Did you have any problem understanding what we did here? Let me know\r
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