Question

Simplifique a Expressão :

$\frac{5}{x^2+x-6} - \frac{2}{x-2}+\frac{4}{x^2-4}$

Answer 1

Resposta:

    (-2x - 5) / (x +2).(x + 3)

Explicação passo-a-passo:

.

.  Simplificar:

.

.  5 / (x² + x - 6)  -  2 / (x - 2)  +  4 / (x² - 4)  =

.  5 / (x - 2).(x + 3)  - 2 / (x - 2)  +  4 / (x + 2).(x - 2)  =

.  [ 5 . (x + 2) - 2 . (x + 2).(x + 3)  + 4 . (x + 3) ] / (x+2).(x - 2).(x + 3) =

.  [ 5x + 10 - 2 . (x² + 5x + 6)  +  4x +  12 ] / (x+2).(x - 2).(x + 3)  =

.  [ 9x + 22  - 2x² - 10x - 12 ] / (x + 2).(x - 2).(x + 3)  =

.  ( - 2x² - x  +  10 ) / (x + 2).(x - 2).(x + 3)  =

.  [ (- 2x - 5).(x - 2) ] / (x + 2).(x - 2).(x + 3)  =

.  (- 2x - 5) / (x + 2).(x + 3)

.

(Espero ter colaborado)

Answer 2

Resposta:

$\frac{5}{x {}^{2} + x - 6 } - \frac{2}{x - 2} + \frac{4}{x {}^{2} - 4}$

$\frac{5}{x {}^{2} + 3x - 2x - 6} - \frac{2}{x - 2} + \frac{4}{(x - 2).(x + 2)}$

$\frac{5}{x.(x + 3) - 2(x + 3)} - \frac{2}{x - 2} + \frac{4}{(x - 2).(x + 2)}$

$\frac{5}{(x + 3).(x - 2)} - \frac{2}{x - 2} + \frac{4}{(x - 2).(x + 2)}$

$\frac{5(x + 2) - 2(x + 3).(x + 2) + 4(x + 3)}{(x + 3).(x - 2).(x + 2)}$

$\frac{5x + 10 + ( - 2x - 6).(x + 2) + 4x + 12}{(x + 3).(x - 2).(x + 2)}$

$\frac{5x + 10 - 2x {}^{2} - 4x - 6x - 12 + 4x + 12}{(x + 3).(x - 2).(x + 2)}$

$\frac{ - x + 10 - 2x {}^{2} }{(x + 3).(x - 2).(x + 2)}$

$\frac{ - 2x {}^{2} - x + 10 }{(x + 3).(x - 2).(x + 2)}$

$\frac{ - 2x {}^{2} + 4x - 5x + 10}{(x + 3).(x - 2).(x + 2)}$

$\frac{ - 2x.(x - 2) - 5(x - 2)}{(x + 3).(x - 2).(x + 2)}$

$\frac{ - (x - 2).(2x + 5)}{(x + 3).(x - 2).(x + 2)}$

$\frac{ - (2x + 5)}{(x + 3).(x + 2)}$

$- \frac{2x + 5}{(x + 3).(x + 2)}$

$- \frac{2x + 5}{x {}^{2} + 2x + 3x + 6 }$

$- \frac{2x + 5}{x {}^{2} + 5x + 6 }$