document.write( "Question 817753: Could someone explain to me how to solve:
\n" ); document.write( " $\"+%283%29%2F%28x%2B2%29%2B%281%29%2F%28x-2%29=%287%29%2F%28x%5E2-4%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "I get to: $\"+%28%283%29%28x-2%29%2B%281%29%28x%2B2%29%29%2F%28x%2B2%29%28x-2%29=%287%29%2F%28x%5E2-4%29+\"$
\n" ); document.write( "Then: $\"+%284x-4%29%2F%28x%5E2-4%29+=+7%2F%28x%5E2-4%29+\"$
\n" ); document.write( "And: $\"+%284x-4%29%28x%5E2-4%29+=+7%28x%5E2-4%29+\"$
\n" ); document.write( "Expand: $\"+4x%5E3-16x-4x%5E2%2B16+=+7x%5E2-28+\"$
\n" ); document.write( "Rearrange: $\"+4x%5E3+-11x%5E2-16x%2B44+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "Now I either made a serious mistake somewhere or maybe I just don't know what to do next.
\n" ); document.write( "Equation should have 2 answers
\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #492173 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You did nothing mathematically wrong. The lady is correct.\r\n" );
document.write( "However, you should clear of fractions from the beginning, \r\n" );
document.write( "not work on each side separately and then cross-multiply \r\n" );
document.write( "later.  It just happened to turn out that the denominators\r\n" );
document.write( "on both sides were x²-4, but in other problems that will not\r\n" );
document.write( "necessarily be the case.  So clear of denominators.  You\r\n" );
document.write( "can probably skip the step where the red multiplication\r\n" );
document.write( "and cancelling is below, because it's just a matter or\r\n" );
document.write( "multiplying each numerator by the factors in the LCD that\r\n" );
document.write( "it does not have underneath it.  You will be able to skip\r\n" );
document.write( "down to 3(x-2)+1(x+2) = 7, just by multiplying each numerator\r\n" );
document.write( "by the factors of the LCD which each numerator does not have\r\n" );
document.write( "underneath it.  I put in the extra steps to show what you are\r\n" );
document.write( "actually doing.\r\n" );
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document.write( "Factor {x²-4) as (x-2)(x+2)\r\n" );
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document.write( "Then get a least common denominator of\r\n" );
document.write( "(x-2)(x+2) written as \r\n" );
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document.write( "Then multiply every term by \r\n" );
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document.write( "Then cancel\r\n" );
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document.write( "3(x-2)+1(x+2) = 7     <--- you could skip the above two steps to here\r\n" );
document.write( "                           by multiplying each numerator by the factors\r\n" );
document.write( "                           in the LCD which are not underneath it.\r\n" );
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document.write( "3x-6+x+2 = 7\r\n" );
document.write( "4x-4 = 7\r\n" );
document.write( "4x = 11\r\n" );
document.write( " x = \r\n" );
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document.write( "Also there is only one solution.\r\n" );
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document.write( "Edwin

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