Can i have help with these 2 Algebra 2 problems?

Question

Been trying to solve these 2 but have been struggling with it. Here they are:

 

1.) (3x)/(2(x+9)) + (x-4)/(x+3) -------------Simplify the expression.

 

2.)(x-7)/(x^2-8x+15) - (9(x-3))/(x^2-25) -------Simplify the Expression

Answer 1

We can combine these to single fractions by getting common denominators, 

but I'm not so sure that amounts to simplifying them.

 

1.) (3x)/(2(x+9)) + (x-4)/(x+3)

 

      3x/(2x+18) + (x-4)/(x+3)

   

    3x(x+3)/((2x+18)(x+3)) + (x-4)(2x+18)/(x+3)(2x+18))

 

    (3x² + 9x + 2x² + 10x - 72)/(2x² + 39x + 54)

 

    (5x² + 19x - 72)/(2x² + 39x + 54)

 

 

2.)  (x-7)/(x^2-8x+15) - (9(x-3))/(x^2-25)

 

      (x-7)/((x-5)(x-3)) - (9(x-3))/((x-5)(x+5))

    

       ((x-7)(x+5))/((x-5)(x-3)(x+5)) - (9(x-3)(x-3))/((x-5)(x+5)(x-3))

 

      ((x²-2x-35)-9(x²-6x+9))/((x-5)(x+5)(x-3))

 

      (x² - 2x - 35 - 9x² + 54x - 81)/((x-5)(x+5)(x-3))

 

      (-8x² + 52x - 116)/((x-5)(x+5)(x-3))

 

      -4(2x² - 13x + 29)/((x-5)(x+5)(x-3))