Вопрос:

Сократить дроби (Вариант №2): 1) \(\frac{39ab^2}{13a^3b}\) 2) \(\frac{42mn^4}{56mn^7}\) 3) \(\frac{a^2-9}{a^2-3a}\) 4) \(\frac{4-m^2}{2m+m^2}\) 5) \(\frac{xy}{xy-x^2y}\) 6) \(\frac{16-m^2}{8m-2m^2}\) 7) \(\frac{mn-m^2}{m-mn}\) 8) \(\frac{p^2+7p}{p^2+14p+49}\) 9) \(\frac{b-5}{25-b^2}\) 10) \(\frac{a^2-16}{16-8a+a^2}\) 11) \(\frac{3xy-2x-3y+2}{x^2-2x+1}\)

Ответ:

Решение варианта №2: 1) \(\frac{39ab^2}{13a^3b} = \frac{3b}{a^2}\) 2) \(\frac{42mn^4}{56mn^7} = \frac{3}{4n^3}\) 3) \(\frac{a^2-9}{a^2-3a} = \frac{(a-3)(a+3)}{a(a-3)} = \frac{a+3}{a}\) 4) \(\frac{4-m^2}{2m+m^2} = \frac{(2-m)(2+m)}{m(2+m)} = \frac{2-m}{m}\) 5) \(\frac{xy}{xy-x^2y} = \frac{xy}{xy(1-x)} = \frac{1}{1-x}\) 6) \(\frac{16-m^2}{8m-2m^2} = \frac{(4-m)(4+m)}{2m(4-m)} = \frac{4+m}{2m}\) 7) \(\frac{mn-m^2}{m-mn} = \frac{m(n-m)}{m(1-n)} = \frac{n-m}{1-n}\) 8) \(\frac{p^2+7p}{p^2+14p+49} = \frac{p(p+7)}{(p+7)^2} = \frac{p}{p+7}\) 9) \(\frac{b-5}{25-b^2} = \frac{b-5}{(5-b)(5+b)} = \frac{-(5-b)}{(5-b)(5+b)} = -\frac{1}{5+b}\) 10) \(\frac{a^2-16}{16-8a+a^2} = \frac{(a-4)(a+4)}{(a-4)^2} = \frac{a+4}{a-4}\) 11) \(\frac{3xy-2x-3y+2}{x^2-2x+1} = \frac{x(3y-2)-(3y-2)}{(x-1)^2} = \frac{(x-1)(3y-2)}{(x-1)^2} = \frac{3y-2}{x-1}\)
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