SOLUTION: (x-1 / x^2+2x)- (2(x-3) / x^2-4 ) + (x-3 / x^2 - 2x) I am not sure how to simplify it when there are 3 denominators and there are addition and subtraction signs between them.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x-1 / x^2+2x)- (2(x-3) / x^2-4 ) + (x-3 / x^2 - 2x) I am not sure how to simplify it when there are 3 denominators and there are addition and subtraction signs between them.      Log On


   

Question 891501: (x-1 / x^2+2x)- (2(x-3) / x^2-4 ) + (x-3 / x^2 - 2x)
I am not sure how to simplify it when there are 3 denominators and there are addition and subtraction signs between them.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume you neglected some parentheses, and what you have is this:

%28x-1%29%2F%28x%5E2%2B2x%29-%282%28x-3%29%2F%28x%5E2-4%29%29%2B%28x-3%29%2F%28x%5E2-2x%29
This is the listing of denominators:
x(x+2), (x+2)(x-2), x(x-2).
The lowest common denominator is x%28x%2B2%29%28x-2%29. Bring each summed expression to higher terms having
this lowest common denominator. The action is to multiply each expression by the appropriate factor
of 1.




%28%28x-1%29x%28x-2%29-2%28x-3%29x%2B%28x-3%29x%28x%2B2%29%29%2F%28x%28x%2B2%29%28x-2%29%29

%28x%28x%5E2-3x%2B2%29-2x%5E2%2B6x%2Bx%28x%5E2-x-6%29%29%2F%28x%28x%2B2%29%28x-2%29%29

%28x%5E3-3x%5E2%2B2x-2x%5E2%2B6x%2Bx%5E3-x%5E2-6x%29%2F%28x%28x%2B2%29%28x-2%29%29

%282x%5E3-3x%5E2-2x%5E2-x%5E2%2B2x%29%2F%28x%28x%2B2%29%28x-2%29%29

%282x%5E3-6x%5E2%2B2x%29%2F%28x%28x%2B2%29%28x-2%29%29

2x%28x%5E2-3x%2B2%29%2F%28x%28x%2B2%29%28x-2%29%29

%282x%28x-1%29%28x-2%29%29%2F%28x%28x%2B2%29%28x-2%29%29



highlight%28%282%28x-1%29%29%2F%28x%2B2%29%29

The first step is appearing strangely. That is not the way the rendering should make it appear.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1 / x^2+2x)- (2(x-3) / x^2-4 ) + (x-3 / x^2 - 2x)
I am not sure how to simplify it when there are 3 denominators and there are addition and subtraction signs between them.


  

 --------- Factoring denominators 

 ------ Multiplying by LCD, x(x - 2)(x + 2) 

%28x%5E2+-+3x+%2B+2+-+2x%5E2+%2B+6x+%2B+x%5E2+-+x+-+6%29%2Fx%28x+-+2%29%28x+%2B+2%29

%28x%5E2+-+2x%5E2+%2B+x%5E2+-+3x+%2B+6x+-+x+%2B+2+-+6%29%2Fx%28x+-+2%29%28x+%2B+2%29

%282x+-+4%29%2Fx%28x+-+2%29%28x+%2B+2%29______%282%28x+-+2%29%29%2Fx%28x+-+2%29%28x+%2B+2%29_____%282cross%28%28x+-+2%29%29%29%2Fcross%28%28x+-+2%29%29x%28x+%2B+2%29______highlight_green%28highlight_green%282%2F%28x%28x+%2B+2%29%29%29%29, or highlight_green%28highlight_green%282%2F%28x%5E2+%2B+2x%29%29%29