Question

Решите, пожалуйста !

Answer 1

$1)\frac{a^{2}-81 }{a^{2}-12a+36}:\frac{a^{2}+9a}{a-6}=\frac{(a-9)(a+9)}{(a-6)^{2}} *\frac{a-6}{a(a+9)}=\frac{a-9}{a-6}\\\\2)\frac{x^{2}-49}{x+7}=-14\\\\\frac{(x+7)(x-7)}{x+7}=-14\\\\x-7=-14;x\neq-7\\\\x=-7\\\\Otvet: \oslash$

решений нет

$3)\frac{a+1}{a-1}-\frac{4a}{a^{2}-1 }=\frac{a+1}{a-1}-\frac{4a}{(a-1)(a+1)} =\frac{a^{2}+2a+1-4a }{(a-1)(a+1)}=\frac{a^{2}-2a+1}{(a-1)(a+1)}=\frac{(a-1)^{2}}{(a-1)(a+1)}=\frac{a-1}{a+1}=\frac{a-1}{a+1}\\\\\frac{a-1}{a+1}:\frac{a-1}{a^{2} +a}=\frac{a-1}{a+1}*\frac{a(a+1)}{a-1}=a\\\\Otvet:\boxed{a}$

$4)\frac{72a^{7}b^{16}}{c^{10}}:(24a^{3}b^{16}}c^{8})=\frac{72a^{7}b^{16}}{c^{10}*24a^{3}b^{16}c^{8}}=\frac{3a^{4}}{c^{18}}\\\\Otvet.\boxed{\frac{3a^{4}}{c^{18}}}$