document.write( "Question 150026: Solve and check all proposed solutions. \"%28x-4%29%2F%28x%2B1%29-10%2F%28x%5E2-1%29=0\" \n" ); document.write( "
Algebra.Com's Answer #110115 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"%28x-4%29%2F%28x%2B1%29-%2810%29%2F%28x%5E2-1%29=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%2F%28x%2B1%29-%2810%29%2F%28%28x-1%29%28x%2B1%29%29=0\" Factor \"x%5E2-1\" to get \"%28x-1%29%28x%2B1%29\"\r
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\n" ); document.write( "\n" ); document.write( "Notice how the LCD is \"%28x-1%29%28x%2B1%29\"\r
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\n" ); document.write( "\n" ); document.write( " Multiply both sides by the LCD \"%28x-1%29%28x%2B1%29\" to clear the fractions.\r
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\n" ); document.write( "\n" ); document.write( " Distribute. Notice how the denominators cancel.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-1%29%28x-4%29-10=%28x-1%29%28x%2B1%29%280%29\" Simplify\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-1%29%28x-4%29-10=0\" Multiply the terms on the right side to get 0\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-5x%2B4-10=0\" FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-5x-6=0\" Combine like terms.\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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29\" Plug in \"a=1\", \"b=-5\", and \"c=-6\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29\" Negate \"-5\" to get \"5\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+25-4%281%29%28-6%29+%29%29%2F%282%281%29%29\" Square \"-5\" to get \"25\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+25--24+%29%29%2F%282%281%29%29\" Multiply \"4%281%29%28-6%29\" to get \"-24\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F%282%281%29%29\" Rewrite \"sqrt%2825--24%29\" as \"sqrt%2825%2B24%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29\" Add \"25\" to \"24\" to get \"49\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+49+%29%29%2F%282%29\" Multiply \"2\" and \"1\" to get \"2\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+7%29%2F%282%29\" Take the square root of \"49\" to get \"7\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B+7%29%2F%282%29\" or \"x+=+%285+-+7%29%2F%282%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812%29%2F%282%29\" or \"x+=++%28-2%29%2F%282%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+6\" or \"x+=+-1\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the possible answers are \"x+=+6\" or \"x+=+-1\"\r
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\n" ); document.write( "\n" ); document.write( "However, we need to check them first.\r
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\n" ); document.write( "\n" ); document.write( "Check:\r
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\n" ); document.write( "\n" ); document.write( "Let's test the first solution \"x+=+6\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%2F%28x%2B1%29-%2810%29%2F%28x%5E2-1%29=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"%286-4%29%2F%286%2B1%29-%2810%29%2F%286%5E2-1%29=0\" Plug in \"x+=+6\".\r
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\n" ); document.write( "\n" ); document.write( "\"%286-4%29%2F%286%2B1%29-%2810%29%2F%2836-1%29=0\" Square 6 to get 36\r
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\n" ); document.write( "\n" ); document.write( "\"%282%29%2F%287%29-%2810%29%2F%2835%29=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"%2810%29%2F%2835%29-%2810%29%2F%2835%29=0\" Multiply \"2%2F7\" by \"5%2F5\"\r
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\n" ); document.write( "\n" ); document.write( "\"%280%29%2F%2835%29=0\" Combine the fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"0=0\" Reduce. Since the equation is true, this means that \"x+=+6\" is a solution.\r
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\n" ); document.write( "\n" ); document.write( "Let's test the second solution \"x+=+-1\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-4%29%2F%28x%2B1%29-%2810%29%2F%28x%5E2-1%29=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"%281-4%29%2F%281%2B1%29-%2810%29%2F%28%28-1%29%5E2-1%29=0\" Plug in \"x+=+-1\".\r
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\n" ); document.write( "\n" ); document.write( "\"%281-4%29%2F%281%2B1%29-%2810%29%2F%281-1%29=0\" Square -1 to get 1\r
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\n" ); document.write( "\n" ); document.write( "\"%28-3%29%2F%282%29-%2810%29%2F%280%29=0\" Combine like terms.\r
\n" ); document.write( "\n" ); document.write( "Since division by zero is undefined, this means that \"x+=+-1\" is not a solution.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solution to \"%28x-4%29%2F%28x%2B1%29-%2810%29%2F%28x%5E2-1%29=0\" is \"x=6\"\r
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