Question

Иррациональное уравнение: 2х/х-5 - х^2+15x/х^2-25 = 0

Answer 1

2x/x-5-x²+15x/x²-25=2x(x+5)-x²-15x/(x-5)(x+5)=2x²+10x-x²-15x/(x-5)(x+5)=
x²-5x/(x-5)(x+5)=x(x-5)/(x-5)(x+5)=x/(x+5)

Answer 2

$\frac{2x}{x-5}- \frac{x^2+15x}{x^2-25}=0 \\\\\frac{2x}{x-5}- \frac{x^2+15x}{(x-5)(x+5)}=0\; |*(x-5)(x+5) \neq 0,\; \; x \neq б5\\\\2x(x+5)-(x^2+15x)=0\\2x^2+10x-x^2-15x=0\\x^2-5x=0\\x(x-5)=0\\x_1=0; \; \; \; x_2=5\\.\; \; \; \; \; \; \; \; \; \; \; \;\; \; x \neq б5\\\\x=0$