Question

х²+5х/(х-5)²:(5/х+5+х²+25/х²-25-5/5-х)
помогите
пжж​

Answer 1

$\displaystyle\bf\\\frac{x^{2}+5x }{(x-5)^{2} } :\Big(\frac{5}{x+5} +\frac{x^{2} +25}{x^{2} -25} -\frac{5}{5-x}\Big)= \\\\\\=\frac{x^{2}+5x }{(x-5)^{2} } :\Big(\frac{5}{x+5} +\frac{x^{2} +25}{(x -5)(x+5)} +\frac{5}{x-5}\Big)= \\\\\\=\frac{x^{2} +5x}{(x-5)^{2} } :\frac{5\cdot(x-5)+x^{2} +25+5\cdot(x+5)}{(x-5)(x+5)} =\\\\\\=\frac{x^{2} +5x}{(x-5)^{2} } :\frac{5x-25+x^{2} +25+5x+25}{(x-5)(x+5)} =\frac{x^{2} +5x}{(x-5)^{2} } :\frac{x^{2} +10x+25}{(x-5)(x+5)} =$

$\displaystyle\bf\\=\frac{x(x+5)}{(x-5)^{2} } \cdot\frac{(x-5)(x+5)}{(x+5)^{2} } =\frac{x}{x-5}$