Question

Решите все которые зачеркнуты не надо​

Answer 1

2)

а)

$\frac{3}{x^{2}-2x} *\frac{2x-4}{x} =\frac{3}{x(x-2)} *\frac{2(x-2)}{x} =\frac{6}{x^{2}}$

б)

$\frac{a-2b}{12c} *\frac{18c^{2}}{2b-a} =\frac{a-2b}{12c}*\frac{18c^{2}}{-(a-2b)} =-\frac{3c}{2}$

в)

$\frac{x^{2}-16}{8x^{3}} *\frac{4x}{x+4} =\frac{(x-4)(x+4)}{8x^{3}} *\frac{4x}{x+4}=\frac{x-4}{2x^{2}}$

г)

$\frac{5-y}{2y} *\frac{3y^{2}}{y^{2}-25} =\frac{-(y-5)}{2y} *\frac{3y^{2}}{(y-5)(y+5)} =-\frac{3y}{2(y+5)} =-\frac{3y}{2y+10}$

д)

$\frac{c^{2}+4c+4}{2c-6} *\frac{c^{2}-9}{5c+10} =\frac{(c+2)^{2}}{2(c-3)} *\frac{(c-3)(c+3)}{5(c+2)} =\frac{(c+2)(c+3)}{10} =\frac{c^{2}+5c+6}{10}$

е)

$(3a-6b)*\frac{a+2}{a^{2}-4b^{2}} =3(a-2b)*\frac{a+2}{(a-2b)(a+2b)} =\frac{3(a+2)}{a+2b} =\frac{3a+6}{a+2b}$

2)

а)

$(-\frac{16x^{2}}{27y^{3}} )^{2}*(\frac{9y^{2}}{8x^{2}} )^{3}=(-\frac{2^{4}x^{2}}{3^{3}y^{3}} )^{2}*(\frac{3^{2}y^{2}}{2^{3}x^{2}} )^{3}=\frac{2^{8}x^{4}}{3^{6}y^{6}} *\frac{3^{6}y^{6}}{2^{9}x^{6}} =\frac{1}{2x^{2}}$

б)

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