Question

алгебра задание с иксами в скобках​

Answer 1

$(\frac{x+2}{x^{2}-2x+1}-\frac{x-2}{x^{2}-1} ):(\frac{x+2}{x^{2}-1} -\frac{x-2}{x^{2}+2x+1}) =\\\\=(\frac{x+2}{(x-1)^{2}}-\frac{x-2}{(x-1)(x+1)} ):(\frac{x+2}{(x-1)(x+1)}-\frac{x-2}{(x+1)^{2}} )=(\frac{(x+2)(x+1)}{(x+1)(x-1)^{2}} -\frac{(x-2)(x-1)}{(x+1)(x-1)^{2}} ):\\\\:(\frac{(x+2)(x+1)}{(x-1)(x+1)^{2}}-\frac{(x-2)(x-1)}{(x-1)(x+1)^{2}} )=(\frac{x^{2}+3x+2}{(x^{2}-1)(x-1)} -\frac{x^{2}-3x+2}{(x^{2}-1)(x-1)} ):\\\\:(\frac{x^{2}+3x+2}{(x^{2}-1)(x+1)}-\frac{x^{2}-3x+2}{(x^{2}-1)(x+1)} )=$

$=\frac{x^{2}+3x+2-x^{2}+3x-2}{(x^{2}-1)(x-1)} :\frac{x^{2}+3x+2-x^{2}+3x-2}{(x^{2}-1)(x+1)} =\frac{6x}{(x^{2}-1)(x-1)} *\frac{(x^{2}-1)(x+1)}{6x} =\frac{x+1}{x-1}$