Question

Упростите выражение

Answer 1

$\frac{49 - {a}^{2} }{a - 9} \times ( \frac{a}{a - 7} - \frac{2a}{ {a}^{2} - 14a + 49 } ) + \frac{14a}{a - 7} = \\ = \frac{49 - {a}^{2} }{a - 9} \times ( \frac{a}{a - 7} - \frac{2a}{ (a - 7)(a - 7) } ) + \frac{14a}{a - 7} = \\ = \frac{49 - {a}^{2} }{a - 9} \times \frac{ {a }^{2} - 7a - 2a }{ (a - 7)(a - 7) } + \frac{14a}{a - 7} = \\ = \frac{ (7 - a)(7 - a)(a - 9 )a }{ (a - 7)(a - 7)(a - 9) } + \frac{14a}{a - 7} = \\ = a+ \frac{14a}{a - 7} = \frac{ {a}^{2} - 7a + 14a }{a - 7} = \frac{a(a + 7)}{a - 7} = \\ = \frac{ {a}^{2} + 7a }{a - 7}$

Answer 2

$1)\frac{a}{a-7}-\frac{2a}{a^{2}-14a+49 }=\frac{a}{a-7}-\frac{2a}{(a-7)^{2}}=\frac{a*(a-7)-2a}{(a-7)^{2}}=\frac{a^{2}-7a-2a }{(a-7)^{2}}=\frac{a^{2}-9a}{(a-7)^{2}}\\\\2)\frac{49-a^{2}}{a-9}*\frac{a^{2}-9a }{(a-7)^{2}}=\frac{(7-a)(7+a)*a*(a-9)}{(a-9)(a-7)^{2}}=\frac{a(a+7)}{7-a}$

$3)\frac{a(a+7)}{7-a}+\frac{14a}{a-7}=\frac{a^{2}+7a }{7-a}-\frac{14a}{7-a}=\frac{a^{2}+7a-14a }{7-a}=\frac{a^{2}-7a}{7-a}=\frac{a(a-7)}{7-a}=-a$