Question

O valor da expressão
$\frac{x + 4}{9x {}^{2} - 1 } + \frac{5 - x}{9x { }^{2} - 6x + 1}$
é:

a)
$\frac{25 + 1}{(3x + 1)(3x - 1) {}^{2} }$
b)
$\frac{25 + 1}{(3x + 1)(3x - 1) {}^{} }$
c)
$\frac{25 - 1}{(3x + 1)(3x - 1) {}^{2} }$
d)
$\frac{25 + 3}{(3x + 1)(3x - 1) {}^{2} }$
​

Answer 1

Explicação passo-a-passo:

$\frac{x+4}{9x^{2}-1}+\frac{5-x}{9x^{2}-6x+1}$

fatorando o 9x² - 1, fica:  (3x - 1) · (3x + 1)

fatorando o 9x² - 6x + 1, fica:  (3x - 1)²

$\frac{x+4}{(3x-1).(3x+1)}+\frac{5-x}{(3x-1)^{2}}$

o m.m.c. de (3x - 1), (3x + 1) e (3x - 1)² é (3x + 1) · (3x - 1)²

$\frac{(x+4).(3x-1)+(5-x).(3x+1)}{(3x+1).(3x-1)^{2}}$

$\frac{(x.3x+x.(-1)+4.3+4.(-1))+(5.3x+5.1+(-x).3x+(-x).1)}{(3x+1).(3x-1)^{2}}$

$\frac{(3.x^{1+1}-x+12x-4)+(15x+5-3.x^{1+1}-x)}{(3x+1).(3x-1)^{2}}$

$\frac{(3x^{2}+11x-4)+(14x+5-3x^{2})}{(3x+1).(3x-1)^{2}}$

$\frac{3x^{2}+11x-4+14x+5-3x^{2}}{(3x+1).(3x-1)^{2}}$

$\frac{3x^{2}-3x^{2}+11x+14x-4+5}{(3x+1).(3x-1)^{2}}$

$\frac{25x+1}{(3x+1).(3x-1)^{2}}$

alternativa a

Obs.: em todas as alternativas, está faltando o x depois do 25