Question

A expressão 5x+5 sobre x²+4x+3 + 4x-12 sobre x²-9 é igual a quanto?

Answer 1

$\dfrac{5x+5}{x^2+4x+3}+{\dfrac{4x-12}{x^2-9}=\dfrac{(5x+5)(x^2-9)+(4x-12)(x^2+4x+3)}{(x^2+4x+3)(x^2-9)}$

$5x+5=5(x+1)$

$x^2+4x+3=x^2+x+3x+3=x(x+1)+3(x+1)=(x+1)(x+3)$

$4x-12=4(x-3)$

$x^2-9=(x+3)(x-3)$

$\dfrac{5x+5}{x^2+4x+3}+\dfrac{4x-12}{x^2-9}=\dfrac{5(x+1)(x+3)(x-3)+4(x-3)(x+1)(x+3)}{(x+1)(x+3)(x-3)(x+3)}$

$\dfrac{5x+5}{x^2+4x+3}+{\dfrac{4x-12}{x^2-9}=\dfrac{[(x+1)(x+3)(x-3)](5+4)}{[(x+1)(x+3)(x-3)](x+3)}$

$\dfrac{5x+5}{x^2+4x+3}+{\dfrac{4x-12}{x^2-9}=\dfrac{5+4}{x+3}$

$\dfrac{5x+5}{x^2+4x+3}+{\dfrac{4x-12}{x^2-9}=\dfrac{9}{x+3}$

Answer 2

A expressão 5x+5 sobre x²+4x+3 + 4x-12 sobre x²-9 é igual a quanto?
     5x + 5              4x - 12
--------------------  +  ----------------        mmc[(x²+4x+3)(x²-9)] =(x+1)(x+3)(x-3)
  (x² + 4x + 3)         (x² - 9)
                                                                           


   5x +  5                 4x - 12
 ----------------   +     ------------------ 
(x + 1)(X+ 3)           (X - 3)(X + 3)


(x-3)(5x+5) + (x+1)(4x-12)
----------------------------------------------
     (x+1)(x+3)(x-3)


5x² + 5x - 15x - 15   + 4x² - 12x + 4x - 12
-----------------------------------------------------------
         (x+1)(x+3)(x-3)

5x² - 10x - 15         + 4x² - 8x - 12
--------------------------------------------------------
    (x+1)Xx+3)(x-3)

9x² - 18x - 27
--------------------------
(x+1)(x+3)(x-3)


9(x² - 2x -3)
------------------------
(x+1)(x+3)(x-3)

 
9((x+1)(x-3))             9((x+1)(x-3)      :  (x+1)(x-3)                    9
---------------------  =   ----------------------------                       =   --------------
(x+1)(x+3)(x-3)          (x+1)(x+3)(x-3)  : (x+1)(X-3)                  X+3