Question

помогите пожалуйста срочно ​

Answer 1

1.

а)

$\frac{x^{2}-xy}{9y^{2}} :\frac{2x}{3y}=\frac{x(x-y)}{9y^{2}} *\frac{3y}{2x} =\frac{x-y}{6y}$

б)

$\frac{c^{2}+4c}{c^{2}-4} :\frac{3c+12}{c-2} =\frac{c(c+4)}{(c+2)(c-2)} :\frac{3(c+4)}{c-2} =\frac{c(c+4)}{(c+2)(c-2)} *\frac{c-2}{3(c+4)} =\frac{c}{3(c+2)} =\frac{c}{3c+6}$

2.

а)

$\frac{a^{2}-b^{2}}{a^{2}-3a} *\frac{2a-6}{(a+b)^{2}} =\frac{(a-b)(a+b)}{a(a-3)}*\frac{2(a-3)}{(a+b)^{2}} =\frac{2(a-b)}{a(a+b)} =\frac{2a-2b}{a^{2}+ab}$

б)

$\frac{x^{2}-1}{5xy}*\frac{x^{2}y}{1+x} =\frac{(x-1)(x+1)}{5xy}*\frac{x^{2}y}{1+x} =\frac{x(x-1)}{5}=\frac{x^{2}-x}{5}$

3.

а)

$(\frac{1}{y} +\frac{2}{x-y} )*(x-\frac{x^{2}+y^{2}}{x+y} )=(\frac{x-y}{y(x-y)} +\frac{2y}{y(x-y)})*(\frac{x(x+y)}{(x+y)}-\frac{x^{2}+y^{2}}{x+y}) =\\\\=\frac{x-y+2y}{y(x-y)}*\frac{x^{2}+xy-x^{2}-y^{2}}{x+y} = \frac{x+y}{y(x-y)} *\frac{y(x-y)}{x+y} =1$

б)

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