Algebra.Com's Answer #817267 by ikleyn(52799)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Solve the rational equation. If there is more than one correct answer, enter a comma separated list.
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document.write( "6/z−6−2/z+6=5/z^2−36
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document.write( "My interior voice tells me that the equation is\r\n" );
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document.write( "  -  =  .\r\n" );
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document.write( "The domain (the set of alloved values for z) is the entire number line except of two hole points -6 and 6).\r\n" );
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document.write( "Transform equivalently\r\n" );
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document.write( "  =  \r\n" );
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document.write( "  =  \r\n" );
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document.write( "Since we work in the domain, we can cancel (z+6)*(z-6) in the denominators. We get then\r\n" );
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document.write( " 4z + 48 = 5\r\n" );
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document.write( " 4z = 5 - 48\r\n" );
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document.write( " 4z = -43\r\n" );
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document.write( " z =  = -10  = -10.75. ANSWER\r\n" );
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document.write( "Solved.\r
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document.write( "I checked my answer numerically by substituting the found value of z into the original equation. It works correctly.\r
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