Rational Expression and Equations ,Functions

Question

Simplify this rational expression 

 

x^2+3x-7    x^2+5x-9       x^2-6x+14

----------- - ------------- + ---------------

x^2-2x-8     x^2-2x-8         x^2-2x-8

 

 

Answer 1

x^2 + 3x - 7 - x^2 - 5x + 9 + x^2 - 6x + 14 
----------------------------------------------------- =
                    x^2 - 2x - 8

(Let's combine like terms in the numerator)

(x^2 - x^2 + x^2) + (3x - 5x - 6x) + (- 7 + 9 + 14)
-------------------------------------------------------------- =
                        x^2 - 2x - 8

 x^2 - 8x + 16  
------------------ =  
   x^2 - 2x - 8 

   (x - 4)^2
---------------- =
(x - 4)(x + 2)

  x - 4  
--------  and this will be the final answer
  x + 2