Question

$\frac{3}{x + 2} + \frac{2}{x - 2} = \frac{13}{ {x}^{2} - 4}$
помогите решить за баллы

Answer 1

$\frac{3}{x+2} +\frac{2}{x-2} =\frac{13}{x^2-4} ;x\neq -2;x\neq 2\\ \\3(x-2)+2(x+2)=13\\ \\ 3x-6+2x+4=13\\ \\ 5x=15\\ \\OTVET :x=3$

Answer 2

$\frac{3}{x + 2} + \frac{2}{x - 2} = \frac{13}{ {x}^{2} - 4} ; \: x \neq -2, \: x \neq 2\\ \\ \frac{3}{x + 2} + \frac{2}{x - 2} = \frac{13}{ {x}^{2} - 4} = 0 \\ \\ \frac{3}{x + 2} + \frac{2}{x - 2} - \frac{13}{(x - 2)(x + 2)} = 0 \\ \\ \frac{3(x - 2) + 2(x + 2) - 13}{(x - 2)(x + 2)} = 0 \\ \\ \frac{3x - 6 + 2x + 4 - 13}{(x - 2)(x + 2)} = 0 \\ \\ \frac{5x + 15}{(x - 2)(x + 2)} = 0 \\ \\ 5x - 15 = 0 \\ \\ 5x = 15 \\ \\ x = 15 \div 5 \\ \\ x = 3; \: x \neq -2, \: x \neq 2$