Question

Даю 40 баллов за пример 6 класса.

Answer 1

$frac{ a^{2} -49}{a+2} * frac{1}{ a^{2}+7a } - frac{ a^{2}+14a+49 }{ a^{3} -4 a^{2}+4a } : frac{a+7}{a-2} + (frac{4}{a-2}) ^{2} = ? \ \ 1) frac{ a^{2} -49}{a+2} * frac{1}{ a^{2}+7a } = frac{(a-7)(a+7)}{a+2} * frac{1}{a(a+7)} = frac{a-7}{a(a+2)} \ \ 2) frac{ a^{2}+14a+49 }{ a^{3} -4 a^{2}+4a } : frac{a+7}{a-2}= frac{(a+7) ^{2} }{a(a-2)(a-2) } * frac{a-2}{a+7} = frac{a+7}{a(a-2)}$
$3)frac{a-7}{a(a+2)}-frac{a+7}{a(a-2)}= frac{(a-7)(a-2)}{a(a+2)(a-2)} - frac{(a+7)(a+2)}{a(a+2)(a-2)} = frac{ a^{2} -9a+14-( a^{2}+9a+14) }{a(a+2)(a-2)} =\ \=frac{a^{2}-9a+14- a^{2}-9a-14}{a(a+2)(a-2)}=frac{-18a}{a(a+2)(a-2)} \ \ 4)(frac{4}{a-2})^{2}=frac{4}{a-2}*frac{4}{a-2}=frac{16}{(a-2)^{2}}$
$\ 5)frac{-18a}{a(a+2)(a-2)}+frac{16}{(a-2)^{2}}=frac{-18a(a-2)}{a(a+2)(a-2)^{2}}+frac{16a(a+2)}{a(a+2)(a-2)^{2}}= \ \ =frac{-18a(a-2)+16a(a+2)}{a(a+2)(a-2)^{2}}= frac{-18a^{2}+36a+16a^{2}+32a}{a(a+2)(a-2)^{2}} = frac{-2a^{2}+68a }{a(a+2)(a-2)^{2}} = \ \ = frac{-2a(a-34)}{a(a+2)(a-2)^{2}} = frac{-2(a-34)}{(a+2)(a-2)^{2}} = frac{-2a+68}{ a^{3} -2a^{2} -4a+8}$