Question

Пожалуста помогите срочно!
(Даю 27баллов) ​

Answer 1

87.

1)

$(\frac{a}{2}-\frac{a}{3} )*\frac{1}{a^{2}} =(\frac{3a}{6} -\frac{2a}{6} )*\frac{1}{a^{2}}=\frac{a}{6} *\frac{1}{a^{2}}=\frac{1}{6a}$

2)

$\frac{a^{2}}{3} *(\frac{2}{a} +\frac{2}{a^{2}} )=\frac{a^{2}}{3}*(\frac{2a}{a^2}} +\frac{2}{a^{2}} )=\frac{a^{2}}{3} *\frac{2a+2}{a^{2}} =\frac{2a+2}{3}$

3)

$\frac{a-b}{a+b} (\frac{a}{5} +\frac{b}{5} )=\frac{a-b}{a+b}*\frac{a+b}{5} =\frac{a-b}{5}$

4)

$\frac{ab}{a-b} (\frac{1}{b} -\frac{1}{a} )=\frac{ab}{a-b} *\frac{a-b}{ab} =1$

5)

$1:(1+\frac{1}{a} )=1:\frac{a+1}{a} =\frac{a}{a+1}$

6)

$b:(b+\frac{1}{b} )=b:\frac{b^{2}+1}{b} =\frac{x^{2}}{x^{2}+1}$

88.

1)

$(1+\frac{1}{a} ):(1-\frac{1}{a} )=\frac{a+1}{a} :\frac{a-1}{a} =\frac{a+1}{a}*\frac{a}{a-1} =\frac{a+1}{a-1}$

2)

$(a+\frac{a}{b} )(a-\frac{a}{b} )=a^{2}-(\frac{a}{b})^{2}=a^{2}-\frac{a^{2}}{b^{2}} =\frac{a^{2}b^{2}-a^{2}}{b^{2}}$

3)

$(\frac{b}{a} +\frac{a}{b} -2):(\frac{1}{b} -\frac{1}{a} )=(\frac{b^{2}}{ab}+\frac{a^{2}}{ab}-\frac{2ab}{ab} ):\frac{a-b}{ab} =\frac{(a-b)^{2}}{ab} *\frac{ab}{a-b} =a-b$

4)

$(\frac{m}{n}+\frac{n}{m}+ 2 )(1+\frac{m-n}{m+n} )=\frac{m^{2}+n^{2}+2mn}{mn} *\frac{m+n+m-n}{m+n} =\frac{(m+n)^{2}}{mn} *\frac{2m}{m+n} =\frac{2m+2n}{n}$