document.write( "Question 85436: Solve:\r
\n" ); document.write( "\n" ); document.write( "x/x-9 -4=9/x-9 \n" ); document.write( "

Algebra.Com's Answer #61627 by scianci(186) $\"\"$ $\"About$

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First, multiply everything by x - 9:\r
\n" ); document.write( "\n" ); document.write( "(x - 9)( $\"x%2F%28x+-+9%29\"$ ) - 4(x - 9) = (x - 9) $\"9%2F%28x+-+9%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Denominators cancel out:\r
\n" ); document.write( "\n" ); document.write( "x - 4(x - 9) = 9\r
\n" ); document.write( "\n" ); document.write( "Distributive property:\r
\n" ); document.write( "\n" ); document.write( "x - 4x + 36 = 9\r
\n" ); document.write( "\n" ); document.write( "Combine like terms:\r
\n" ); document.write( "\n" ); document.write( "-3x + 36 = 9\r
\n" ); document.write( "\n" ); document.write( "Subtract 36 from both sides:\r
\n" ); document.write( "\n" ); document.write( "-3x = -27\r
\n" ); document.write( "\n" ); document.write( "Divide both sides by -3:\r
\n" ); document.write( "\n" ); document.write( "x = 9 [potentially]\r
\n" ); document.write( "\n" ); document.write( "Check for extraneous solutions [denominator can't = 0]:\r
\n" ); document.write( "\n" ); document.write( "x - 9 = 9 - 9 = 0. Since this = 0, the solution x = 9 is extraneous. Since this is the only potential solution obtained to begin with, the equation has no solution. \n" ); document.write( "

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