solving rational equations (ANSWER NEEDED ASAP)

Question

x^2+x-6/x^2+9x+14   -   8/x+7

solve(subtraction) and find out what x can't be? answer needed ASAP

Answer 1

Assuming  (x^2 + x - 6)                   8

                ----------------- -      --------------

                x^2 +9x + 14                x+ 7

 

 

Factoring:

 

                (  x     +    3)(x     -    2   )               8

              ----------------------------------   -  --------------

                  ( x     +    7)(x    +       2   )     (x+7)

 

The second fraction DOES NOT have (x+2), so we put (x+2) on the top and bottom for common denominator

 

The denominator is (x+7)(x+2) 

 

The top becomes (x+3)(x-2) - 8(x+2)

                            =  x^2 +x - 6 - 8x - 16

 

                            = x^2 - 7x - 22

               

                               and cannot be factored any further

 

      The final answer is:

 

    x^2 - 7x - 22

----------------------

  x^2 + 9x + 14