Question

Alguien me podria explicar cómo hago
$\frac{3x - 1}{x + 2} - \frac{2x}{x - 2} = \frac{1}{{x}^{2} - 4 } + 3$
Por favor que no entiendo nada

Answer 1

$\frac{3x-1}{X+2}- \frac{2x}{x-2}= \frac{1}{x2-4}+3$

$\frac{(3x-1)(x-2)-2x(x+2)}{x2-4}= \frac{1+3(x2-4)}{x2-4}$

3$x^{2} -6x-x+2-2x^{2} -4x=1+3x^{2} -12$

$x^{2} -11x+2=-11+3x^{2}$

$x^{2} -11x+2+11-3x^{2} =0$

-2$x^{2} +11x+13=0$

2$x^{2} -11x -13=0$

2(2$x^{2} -11x-13)/2$= 0

(4$x^{2} -11(2x)-26)/2$= 0

((2x-13)(2x+2))/2=0

$\frac{(2x-13)2(x+1)}{2}$=0

(2x-13)(x+1)=0

2x - 13 = 0

x = 13/2

x + 1 = 0

x = -1