document.write( "Question 1135174: I done the following rational expression addition and subtraction 4*x/(x^2-1)+3*x/(1-x)-4/(x-1) and had some issues with it , I have seen the full answer and got stuck on how some things were arrived at . I wonder if some one would kindly shed some light on the following. 1, in both the second term -3*x/1-x and third term -4/(x-1) could a greater explanation of how or why the denominators are allocated to there numerators? I would have thought that the third term -4/(x-1) would equal -4*(-x+1)*(x+1)/(x+1)*(-x+1)*(x-1) instead of -4*(x+1)*(x-1) ? 2, and finally an explanation of how factoring the total numerator is achieved ? As all this would be much appreciated kind regards mike. \n" ); document.write( "

Algebra.Com's Answer #752742 by josgarithmetic(39623) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4%2Ax%2F%28x%5E2-1%29%2B3%2Ax%2F%281-x%29-4%2F%28x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "understand that $\"%28-1%29%281-x%29=-1%2Bx=x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now your expression is equivalent to
\n" ); document.write( " $\"4%2Ax%2F%28x%5E2-1%29-3%2Ax%2F%28x-1%29-4%2F%28x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Note that simplest common denominator is $\"%28x%2B1%29%28x-1%29\"$ .
\n" ); document.write( "Bring each separate rational expression to \"higher terms\" for this denominator. \n" ); document.write( "

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