Question

99 БАЛЛОВ!!!!!!!!! Упростите выражение
$frac{c+5}{c^2-64} : ( frac{4}{c+8} - frac{12}{c^2+16c+64} )+ frac{4}{8-c}$

Answer 1

$frac{c+5}{c^2-64} : ( frac{4}{c+8} - frac{12}{c^2+16c+64} )+ frac{4}{8-c}= \ \ = frac{c+5}{c^2-64}:( frac{4}{c+8}- frac{12}{(c+8)^2})+ frac{4}{8-c}= \ \=frac{c+5}{c^2-64}: frac{4(c+8)-12}{(c+8)^2}+ frac{4}{8-c}= \ \=frac{c+5}{c^2-64}: frac{4c+32-12}{(c+8)^2} + frac{4}{8-c}= \ \=frac{c+5}{c^2-64}:frac{4c+20}{(c+8)^2}+ frac{4}{8-c} = frac{(c+5)*(c+8)^2}{(c-8)(c+8)*4(c+5)}- frac{4}{c-8}= \ \ = frac{c+8}{4(c-8)} - frac{4}{c-8}= frac{c+8-16}{4(c-8)}=$

$=frac{c-8}{4(c-8)} = frac{1}{4} =0,25$

Ответ: $0,25$