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statuscvo [17]
3 years ago
5

(2x-4)/(x^2-4)+(x-3)/(x^2+5x+6) simplify

Mathematics
1 answer:
maria [59]3 years ago
4 0

Answer:

      3(x + 1)

= ------------------

   (x +2)(x + 3)

Step-by-step explanation:

 (2x-4)                    (x-3)

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

(x^2-4)              (x^2+5x+6)

      (2x-4)                    (x-3)

= -------------- ----+ ------------------------

 (x + 2)(x - 2)           (x + 3)(x + 2)

GCF = (x +2)(x - 2)(x + 3)

    (2x - 4)(x + 3) + (x - 3)(x - 2)

= ------------------------------------------

         (x +2)(x - 2)(x + 3)

    2x^2 + 6x - 4x - 12 + x^2 -2x - 3x + 6

= -----------------------------------------------------------

               (x +2)(x - 2)(x + 3)

    3x^2  -  3x   -6

= --------------------------

   (x +2)(x - 2)(x + 3)

    3(x^2  -  x   - 2)

= --------------------------

   (x +2)(x - 2)(x + 3)

    3(x - 2)(x + 1)

= --------------------------

   (x +2)(x - 2)(x + 3)

      3(x + 1)

= ------------------

   (x +2)(x + 3)

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