document.write( "Question 826264: Solve for x.
\n" ); document.write( "3/(x-1)+3/(x+1)=4 \n" ); document.write( "
Algebra.Com's Answer #497993 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Solve for x.\r\n" );
document.write( "\"3%2F%28x-1%29%2B3%2F%28x%2B1%29=4\"\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "THis problem will be easier to solve if we clear the denominators from each term. Multiply\r\n" );
document.write( "each side of the equation by (x-1)(x+1), the LCD (least common denominator.)\r\n" );
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document.write( "We can eliminate the common factors in the numerator and denominator because any \r\n" );
document.write( "non-zero expression divided by itself equals 1.\r\n" );
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document.write( "Simplify.\r\n" );
document.write( "\"3%28x%2B1%29%2B3%28x-1%29=4%2A%28x-1%29%28x%2B1%29\"\r\n" );
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document.write( "Use the distributive property to clear the parentheses.\r\n" );
document.write( "\"3x%2B3%2B3x-3=4x%5E2-4\"\r\n" );
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document.write( "This is a quadratic equation because the 4x-squared term has the highest degree. To solve it, \r\n" );
document.write( "set this equation equal to zero by moving all terms to the left side.\r\n" );
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document.write( "\"-4x%5E2%2B6x%2B4=0\"\r\n" );
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document.write( "I always try to factor these first because I like factoring and the quadratic formula is not my \r\n" );
document.write( "friend! The quadratic formula will always work, though. Factoring, only sometimes.\r\n" );
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document.write( "Find the factors of x-squared term (-4x^2):\r\n" );
document.write( "-4x,x\r\n" );
document.write( "4,-x\r\n" );
document.write( "2x,-2x\r\n" );
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document.write( "Find the factors of the constant term (4):\r\n" );
document.write( "4,1\r\n" );
document.write( "2,2\r\n" );
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document.write( "We are looking for a combination with a sum of the x-term (6x):\r\n" );
document.write( "2x,-2x and 4,1 work because (2x)(4)+(-2x)(1) = 8x - 2x = 6x\r\n" );
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document.write( "Your equation in factored form is\r\n" );
document.write( "\"%282x%2B1%29%28-2x%2B4%29=0\"\r\n" );
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document.write( "Applying the Zero Product Property, we know that either 2x+1=0 or -2x+4=0. Solve these\r\n" );
document.write( "equations.\r\n" );
document.write( "2x + 1 = 0    --->  2x = -1  --->  x = -1/2\r\n" );
document.write( "-2x + 4 = 0  --->  -2x = -4  --->  x = 2\r\n" );
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document.write( "The solutions to your equation are x=-1/2 or x=2.\r\n" );
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document.write( "Check these values in the original equation.\r\n" );
document.write( "\"3%2F%28x-1%29%2B3%2F%28x%2B1%29=4\"\r\n" );
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document.write( "For x=-1/2:\r\n" );
document.write( "\"3%2F%28%28-1%2F2%29-1%29%2B3%2F%28%28-1%2F2%29%2B1%29=4\"\r\n" );
document.write( "\"-2%2B6=4\"\r\n" );
document.write( "\"4=4\"\r\n" );
document.write( "CHECK!\r\n" );
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document.write( "For x=2:\r\n" );
document.write( "\"3%2F%282%29-1%29%2B3%2F%28%282%29%2B1%29=4\"\r\n" );
document.write( "\"3%2B1=4\"\r\n" );
document.write( "\"4=4\"\r\n" );
document.write( "CHECK!\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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