Question

X+2 / x^2-2x+1 * 4x-4 / x^2-4 + 4 / x-1 = 4 / x-2 Доведіть тотожність ПЖ СРОЧНО

Answer 1

$\frac{x+2}{ x^2-2x+1} *\frac{ 4x-4}{x^2-4} +\frac{ 4}{x-1} =\frac{ 4}{x-2} \\\\\\\frac{x+2}{( x-1)^2} *\frac{ 4(x-1)}{(x -2)(x+2)} +\frac{ 4}{x-1} =\frac{ 4}{x-2}\\\\\\ \frac{ 4 }{(x-1)( x -2 ) } +\frac{ 4}{x-1} =\frac{ 4}{x-2} \\\\\\\frac{ 4 +4(x-2)}{(x-1)( x -2 ) } =\frac{ 4}{x-2}\\\\\\\frac{ 4 (1 + x-2)}{(x-1)( x -2 ) } =\frac{ 4}{x-2}$

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