• Предмет: Алгебра
  • Автор: SokaHader
  • Вопрос задан 8 лет назад

номер 41.5
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Ответы

Ответ дал: zhenyaM2002
0
41.5
1.
 frac{a^2 - 25}{a+3} * frac{1}{a^2+5a} - frac{a+5}{a^2-3a} = frac{a^2 - 5^2}{a+3} * frac{1}{a(a+5)} - frac{a+5}{a(a-3)} = \  \ 
= frac{(a-5)(a+5)}{a+3} * frac{1}{a(a+5)} - frac{a+5}{a(a-3)} =  frac{(a-5)(a+5)*1}{(a+3) * a(a+5)} - frac{a+5}{a(a-3)} = \  \ 
=  frac{(a-5)*1*1}{(a+3)*a*1} - frac{a+5}{a(a-3)} =   frac{a-5}{a(a+3)} - frac{a+5}{a(a-3)} = frac{(a-5)(a-3)-(a+5)(a+3)}{a(a+3)(a-3)} =  \  \  \
=  frac{a^2-3a-5a+15 - (a^2+3a+5a+15)}{a(a+3)(a-3)} =  frac{a^2-8a+15-a^2-8a-15}{a(a+3)(a-3)} =  frac{-16a}{a(a+3)(a-3)} =  \  \ 
=  frac{-16}{(a+3)(a-3)} =  -  frac{16}{a^2-3^2} = - frac{16}{a^2 - 9}  \  \ 
1) a = 2 \  \ 
 - frac{16}{2^2 - 9}  = -  frac{16}{4 - 9} =  - frac{16}{-5} =  - ( - 3.2) = 3.2 \  \ 
2) a = - 4 \  \ 
 - frac{16}{(-4)^2 - 9}  =  -  frac{16}{16 - 9} = -  frac{16}{7}  = - 2 frac{2}{7}

2.
 frac{1 - 2x}{2x+1}  +  frac{x^2+3x}{4x^2 - 1} : frac{3+x}{4x+2} = frac{1 - 2x}{2x+1}  +  frac{x(x+3)}{(2x)^2 - 1^2} : frac{3+x}{2(2x+1)} = \  \ 
=  frac{1 - 2x}{2x+1}  +  frac{x(x+3)}{(2x-1)(2x+1)} * frac{2(2x+1)}{x+3} =frac{1 - 2x}{2x+1}  + frac{x(x+3)*2(2x+1)}{(2x-1)(2x+1)(x+3)} = \  \ 
= frac{1 - 2x}{2x+1}  + frac{x*1*2*1}{(2x-1)*1*1} = frac{1 - 2x}{2x+1}  + frac{2x}{2x-1} =  frac{(1-2x)(2x-1) +2x(2x+1)}{(2x+1)(2x-1)} = \  \  \
=  frac{2x-1-4x^2+2x+4x^2+2x}{(2x+1)(2x-1)} =  frac{6x-1}{(2x)^2-1^2} = frac{6x-1}{4x^2 - 1}  \  \ 
1) x = - 1 \  \ 
frac{6*(-1)-1}{4*(-1)^2 - 1}=  frac{- 6 - 1}{4*1 - 1} =  frac{-7}{3} = - 2 frac{1}{3}  \  \ 
2) x = -2.5 \  \ 
frac{6*(-2.5)-1}{4*(-2.5)^2 - 1}=  frac{- 15 - 1}{4 *6.25 - 1}  =  frac{-16}{25 - 1} = frac{-16}{24} = -  frac{2}{3}
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