Cрочно 8 класс тема алгебраические дроби,3 задания обведены

Question 1

Question 2

105. б) $\frac{ b^{2}-ab }{ a^{2} +ad} : \frac{ab}{ d^{2} +ad} = \frac{b(b-a)}{a(a+d)} * \frac{d(d+a)}{ab} = \frac{d(b-a)}{ a^{2} } = \frac{bd-ad}{ a^{2} }$
г) $\frac{a^{2}+4a+4 }{2a-2} * \frac{a^{2}-a }{3a+6}= \frac{ (a+2)^{2} }{2(a-1)} * \frac{a(a-1)}{3(a+2)} = \frac{ (a+2)(a+2) }{2(a-1)} * \frac{a(a-1)}{3(a+2)} = \frac{a(a+2)}{6} =$
$=\frac{ a^{2} +2a}{6}$

107. б) $\frac{2 x^{3}+2 z^{3} }{xz- x^{2} } : \frac{ x^{3}- x^{2} z+x z^{2} }{ x^{2} - z^{2} } = \frac{2( x^{3} + z^{3} )}{-x(x-z)} * \frac{(x-z)(x+z)}{x( x^{2} -xz+ z^{2} )} =$
$= \frac{2(x+z)( x^{2} -xz+ z^{2} )}{-x(x-z)}*\frac{(x-z)(x+z)}{x( x^{2} -xz+ z^{2} )} = \frac{2(x+z)(x+z)}{- x^{2} } =- \frac{2(x+z)^{2} }{ x^{2} }$
г) $\frac{ x^{4}-16 }{ x^{2} -4x+4} : \frac{ x^{3} +8}{x-2} = \frac{( x^{2} -4)( x^{2} +4)}{(x-2)^{2} } * \frac{x-2}{(x+2)( x^{2} -2x+4)} =$
$=\frac{( x-2)(x+2)( x^{2} +4)}{(x-2)^{2} } * \frac{x-2}{(x+2)( x^{2} -2x+4)} = \frac{ x^{2} +4}{ x^{2} -2x+4}$

98. б) $\frac{m n^{2} }{ n^{2} - m^{2} } *( \frac{2}{m} - \frac{2}{n} )= \frac{m n^{2} }{ n^{2} - m^{2} } *( \frac{2n}{mn} - \frac{2m}{mn} )= \frac{m n^{2} }{ n^{2}- m^{2} } * \frac{2n-2m}{mn} =$
$= \frac{m n^{2} }{(n-m)(n+m)} * \frac{2(n-m)}{mn} = \frac{2n}{n+m}$
г) $( \frac{u}{u-v} - \frac{u}{u+v} )* \frac{ u^{2} +uv}{2v} =( \frac{u(u+v)}{(u-v)(u+v)} - \frac{u(u-v)}{(u-v)(u+v)} )* \frac{u(u+v)}{2v} =$
$= \frac{u(u+v)-u(u-v)}{(u-v)(u+v)} * \frac{u(u+v)}{2v} = \frac{ u^{2}+uv- u^{2}+uv }{(u-v)(u+v)} * \frac{u(u+v)}{2v} =$
$= \frac{2uv}{(u-v)(u+v)} * \frac{u(u+v)}{2v} = \frac{u^{2} }{u-v}$
е) $(a+b)^{2} :( \frac{1}{ a^{2} } + \frac{1}{ b^{2} } + \frac{2}{ab} )= (a+b)^{2} : (\frac{ b^{2} }{ a^{2} b^{2} } + \frac{ a^{2} }{ a^{2} b^{2} } + \frac{2ab}{ a^{2} b^{2} } )=$
$= (a+b)^{2} : \frac{ b^{2}+a^{2} +2ab }{ a^{2} b^{2} } = (a+b)^{2} * \frac{ a^{2} b^{2} }{(a+b)^{2} } = a^{2} b^{2}$