Question 76390
The given expression is: 


{{{ ((2x^2 - 3x)/(x^2 - 2x - 63))  +    ((7-x)/(x^2 - 2x - 63))  -   ((x^2 - 3x + 21)/(x^2 - 2x - 63))}}} 



Since the denominators is the same for all the 3 expressions, the LCM will be the smae. That is {{{(x^2 - 2x - 63)}}} 


Hence, the given expression can be written as:  



{{{(2x^2 + 3x + 7 - x - (x^2 - 3x + 21))/(x^2 - 2x - 63)}}}  


This can be written as:  


{{{(2x^2 + 3x + 7 - x - x^2 + 3x - 21)/(x^2 - 2x - 63)}}}


Simplifying this further, we get: 



{{{(x^2 + 5x - 14)/(x^2 - 2x - 63)}}} 


Here, both the numerator and the denominator can be factored and can be written as: 


{{{(x(x + 7) - 2(x + 7))/(x(x - 9) + 7(x - 9))}}} 


This can be written as: 


{{{(x - 2)(x + 7)/(x + 7)(x - 9)}}} 



Here we observe that (x + 7) is present  both in the numerator and the denominator. 


{{{(x + 2)* cross((x + 7))/(x - 9)/cross((x + 7))}}}



Hence, we remain with 


{{{(x + 2)/(x -9)}}}


Thus, the solution.