document.write( "Question 96159: Solve and check for x\r
\n" ); document.write( "\n" ); document.write( "(x/x-2)-(x+1/x)=(8/x^2-2x) \n" ); document.write( "

Algebra.Com's Answer #70077 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Solve and check for x
\n" ); document.write( "(x/x-2)-(x+1/x)=(8/x^2-2x)
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\n" ); document.write( " $\"x%2F%28%28x-2%29%29\"$ - $\"%28%28x%2B1%29%29%2Fx\"$ = $\"8%2F%28%28x%5E2-2x%29%29\"$
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\n" ); document.write( "Factor (x^2 - 2x):
\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( "Multiplying equation by x(x-2) gets rid of the denominators and we 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: removing the brackets changes the signs
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\n" ); document.write( "x + 2 = 8; x^2's eliminated
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\n" ); document.write( "x = 8 - 2\r
\n" ); document.write( "\n" ); document.write( "x = 6
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\n" ); document.write( "Check solution by substituting 6 for x in the original equation:
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\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( ":
\n" ); document.write( " $\"6%2F4\"$ - $\"7%2F6\"$ = $\"8%2F24\"$ = $\"36%2F24\"$ - $\"28%2F24\"$ = $\"8%2F24\"$ Confirms our solution \n" ); document.write( "

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