document.write( "Question 277025: How could I solve this equation dealing with fractions.
\n" ); document.write( "x/x+4 - 2 = 12/x-12
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Algebra.Com's Answer #201760 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%2F%28x%2B4%29+-+2+=+12%2F%28x-12%29\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " Multiply EVERY term by the LCD \"%28x%2B4%29%28x-12%29\" to clear out the fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-12%29%28x%29-+2%28x%2B4%29%28x-12%29=%28x%2B4%29%2812%29\" Simplify \r
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\n" ); document.write( "\n" ); document.write( "\"x%28x-12%29-+2%28x%2B4%29%28x-12%29=12%28x%2B4%29\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "\"x%28x-12%29-+2%28x%5E2-8x-48%29=12%28x%2B4%29\" FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-12x-+2x%5E2%2B16x%2B96=12x%2B48\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-12x-2x%5E2%2B16x%2B96-12x-48=0\" Get every term to the left side.\r
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\n" ); document.write( "\n" ); document.write( "\"-x%5E2-8x%2B48=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"-x%5E2-8x%2B48\" is in the form of \"Ax%5E2%2BBx%2BC\" where \"A=-1\", \"B=-8\", and \"C=48\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"x\":\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29\" Plug in \"A=-1\", \"B=-8\", and \"C=48\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29\" Negate \"-8\" to get \"8\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+64-4%28-1%29%2848%29+%29%29%2F%282%28-1%29%29\" Square \"-8\" to get \"64\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+64--192+%29%29%2F%282%28-1%29%29\" Multiply \"4%28-1%29%2848%29\" to get \"-192\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+64%2B192+%29%29%2F%282%28-1%29%29\" Rewrite \"sqrt%2864--192%29\" as \"sqrt%2864%2B192%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+256+%29%29%2F%282%28-1%29%29\" Add \"64\" to \"192\" to get \"256\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+sqrt%28+256+%29%29%2F%28-2%29\" Multiply \"2\" and \"-1\" to get \"-2\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B-+16%29%2F%28-2%29\" Take the square root of \"256\" to get \"16\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%288+%2B+16%29%2F%28-2%29\" or \"x+=+%288+-+16%29%2F%28-2%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2824%29%2F%28-2%29\" or \"x+=++%28-8%29%2F%28-2%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+-12\" or \"x+=+4\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x+=+-12\" or \"x+=+4\"\r
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\n" ); document.write( "\n" ); document.write( "I'll let you check these solutions.
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