Докажите тождество (24,5x^2-0,5y^2)/(3,5x^2-0,5xy)=(7x+y)/x.

\[\frac{24,5x^{2} - 0,5y^{2}}{3,5x^{2} - 0,5xy} = \frac{7x + y}{x}\]

\[\frac{24,5x^{2} - 0,5y^{2}}{3,5x^{2} - 0,5xy} = \frac{7x + y}{x}\]

\[\frac{0,5 \cdot \left( 49x^{2} - y^{2} \right)}{0,5x(7x - y)} = \frac{7x + y}{x}\]

\[\frac{(7x - y)(7x + y)}{x(7x - y)} = \frac{7x + y}{x}\]

\[\frac{7x + y}{x} = \frac{7x + y}{x}\]

\[Что\ и\ требовалось\ доказать.\]