Question

((5x+y)/(x-5y)+(5x-y)/(x+5y)):(x^2+y^2)/(x^2-25y^2)
каждое действие подробно

Answer 1

    $(\frac{5x+y}{x-5y}+\frac{5x-y}{x+5y}):\frac{x^2+y^2}{x^{2}-25y^2}=$

$=\frac{(5x+y)*(x+5y)+(5x-y)*(x-5y)}{(x-5y)*(x+5y)}:\frac{x^2+y^2}{x^2-25y^2} =$

$=\frac{5x^2+xy+25xy+5y^2+5x^2-xy-25xy+5y^2}{(x-5y)*(x+5y)}:\frac{x^2+y^2}{x^2-25y^2} =$

$=\frac{10x^2+10y^2}{x^2-25y^2}:\frac{x^2+y^2}{x^2-25y^2} =$

$=\frac{10(x^2+y^2)}{x^2-25y^2}*\frac{x^2-25y^2}{x^2+y^2} =$

$=\frac{10(x^2+y^2)*(x^2-25y^2)}{(x^2-25y^2)*(x^2+y^2)}=10$