(2x+1)/(x-1) - (2x-1)/(x+1)

Question

• math heklp

Answer 1

(2x+1)/(x-1) - (2x-1)/(x+1) = ?

 

Multiply through by [(x-1)(x+1)] / [(x-1)(x+1)] and simplify:

 

(x+1)(2x+1) - (x-1)(2x-1)= (2x^2 + x + 2x + 1) - (2x^2 - x - 2x + 1) = (2x^2 + 3x + 1) - (2x^2 - 3x +1)

 

Note the 2x^2 terms cancel out.  Simplifying further, you are left with

 

(3x +1) - (-3x + 1) = 6x

 

Final answer:

 

The simplified expression gives 6x.