Question

Найдите значение
$\frac{y^{2} - 6y + 9 }{y^{2} - 9 } \div \frac{10y - 30}{y ^{2} + 3y}$
при у=70

Answer 1

Упростим выражение:
$\frac{y^2-6y +9}{y^2-9} : \frac{10y-30}{y^2+3y} = \frac{y^2 -2*y*3+3^2}{y^2-3^2} : \frac{10(y-3)}{y(y+3)} = \\ \\ =\frac{(y-3)^2 }{(y-3)(y+3)} * \frac{y(y+3)}{10(y-3)} = \frac{y-3}{y+3} * \frac{y(y+3)}{10(y-3)} = \\ \\ = \frac{y(y-3)(y+3)}{10(y-3)(y+3)} = \frac{y}{10} = \frac{1}{10} *y = 0.1y$

при у= 70   ⇒  0,1 * 70  = 7