SOLUTION: 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

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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.
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!


understand that

Now your expression is equivalent to


Note that simplest common denominator is .
Bring each separate rational expression to "higher terms" for this denominator.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


It appears that you are trying to use

(x+1)(x-1)(-x+1)

as your common denominator.

What you are overlooking is the fact that

(-x+1) = -1(x-1)

So you don't need both (x-1) and (-x+1) in your common denominator.

You will be seeing a lot of problems in which expressions like (2x-3) and (-2x+3) appear. Learn to recognize that kind of thing.

Also, in general, when working with polynomials of any size, it is always far more awkward if any of the leading coefficients are negative.

So in a problem like this, where you have terms of

and

rewrite the first one by multiplying top and bottom by -1, making it



Then you will see that the common denominator you want to use is simply (x+1)(x-1).

=
=


Since that's the specific part of the problem you asked about, I'll leave my response there and assume that you can finish simplifying the expression.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

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.




The LCD is then: - (x + 1)(x - 1), and  becomes:

 ------- Multiplying EACH EXPRESSION by LCD, -(x + 1)(x - 1)

 <==== Same as above

 

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