Предмет: Алгебра, автор: artamoshkinavaleria

Х
$(x ^{2} - 30x + 225) \div x ^{2} - 225$ если х=-2,5
Помогите решить

Ответы

Автор ответа: Reideen

$\displaystyle( {x}^{2} - 30x + 225) \div {x}^{2} - 225 = \\ = \frac{ {x}^{2} - 30x + 225 }{ {x}^{2} } - 225 = \\ = \frac{(x - 15)^{2} }{ {x}^{2} } - 225 = \\ = \bigg( \frac{x - 15}{x}\bigg)^{2} - {15}^{2} = \\ = \bigg( \frac{x - 15}{x} - 15 \bigg) \bigg( \frac{x - 15}{x} + 15 \bigg) = \\ = \bigg(1 - \frac{15}{x} - 15 \bigg) \bigg(1 - \frac{15}{x} + 15 \bigg) = \\ = \bigg( - 14 - \frac{15}{x} \bigg) \bigg( 16- \frac{15}{x} \bigg) = \\ = \bigg( - 14 - \frac{15}{ - 2.5} \bigg) \bigg(16 - \frac{15}{ - 2.5} \bigg) = \\ = \bigg( - 14 + \frac{15}{2.5} \bigg) \bigg(16 + \frac{15}{2.5} \bigg) = \\ = ( - 14 + 6)(16 + 6) = \\ = ( - 8) \times 22 = \\ = - 176$