document.write( "Question 103008: \"3%2F%28x-1%29-6%2F%28x%5E2-1%29=1\" \n" ); document.write( "
Algebra.Com's Answer #75006 by ankor@dixie-net.com(22740)\"\" \"About 
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\"3%2F%28%28x-1%29%29\" - \"6%2F%28%28x%5E2-1%29%29\" = 1
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\n" ); document.write( "You can see that (x^2-1) is the difference of squares so factor that:
\n" ); document.write( "\"3%2F%28%28x-1%29%29\" - \"6%2F%28%28x-1%29%28x%2B1%29%29\" = 1
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\n" ); document.write( "Common denominator would be (x-1)(x+1), multiply equation by that:
\n" ); document.write( "(x-1)(x+1)\"3%2F%28%28x-1%29%29\" - (x-1)(x+1)\"6%2F%28%28x-1%29%28x%2B1%29%29\" = 1(x-1)(x+1)
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\n" ); document.write( "Cancel out the denominators and you have;
\n" ); document.write( "3(x+1) - 6 = (x-1)(x+1)
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\n" ); document.write( "Multiply what's inside the brackets on the left, FOIL the right
\n" ); document.write( "3x + 3 - 6 = x^2 - 1
\n" ); document.write( "3x - 3 = x^2 - 1
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "x^2 - 3x - 1 + 3 = 0
\n" ); document.write( "x^2 - 3x + 2 = 0
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\n" ); document.write( "Factors to:
\n" ); document.write( "(x-2)(x-1) = 0
\n" ); document.write( "Two solutions:
\n" ); document.write( "x = +2
\n" ); document.write( "x = +1
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\n" ); document.write( "However x = 1, cannot be a solution. Note that if you substitute 1 for x,
\n" ); document.write( "both fractions have division by 0
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\n" ); document.write( "x = 2 is the only solution, check by subsitution
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\n" ); document.write( "\"3%2F%28%282-1%29%29\" - \"6%2F%28%282%5E2-1%29%29\" = 1
\n" ); document.write( " 3 - \"6%2F3\" = 1
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