Сократить дроби (Вариант №1): 1) \(\frac{42x^2y}{7xy^3}\) 2) \(\frac{17mn^4}{34mn^6}\) 3) \(\frac{a^2-ab}{a^2-b^2}\) 4) \(\frac{9-m^2}{m^2+3m}\) 5) \(\frac{xy}{xy^2+xy}\) 6) \(\frac{2a^2-6a}{a^2-9}\) 7) \(\frac{a-a^2}{ab-a^2}\) 8) \(\frac{p^2-3p}{p^2-6p+9}\) 9) \(\frac{b-4}{16-b^2}\) 10) \(\frac{a^2-49}{49-14a+a^2}\) 11) \(\frac{ax^2-2x^2-ay^2+2y^2}{ax+ay-2x-2y}\)

Решение варианта №1: 1) \(\frac{42x^2y}{7xy^3} = \frac{6x}{y^2}\) 2) \(\frac{17mn^4}{34mn^6} = \frac{1}{2n^2}\) 3) \(\frac{a^2-ab}{a^2-b^2} = \frac{a(a-b)}{(a-b)(a+b)} = \frac{a}{a+b}\) 4) \(\frac{9-m^2}{m^2+3m} = \frac{(3-m)(3+m)}{m(m+3)} = \frac{3-m}{m}\) 5) \(\frac{xy}{xy^2+xy} = \frac{xy}{xy(y+1)} = \frac{1}{y+1}\) 6) \(\frac{2a^2-6a}{a^2-9} = \frac{2a(a-3)}{(a-3)(a+3)} = \frac{2a}{a+3}\) 7) \(\frac{a-a^2}{ab-a^2} = \frac{a(1-a)}{a(b-a)} = \frac{1-a}{b-a}\) 8) \(\frac{p^2-3p}{p^2-6p+9} = \frac{p(p-3)}{(p-3)^2} = \frac{p}{p-3}\) 9) \(\frac{b-4}{16-b^2} = \frac{b-4}{(4-b)(4+b)} = \frac{-(4-b)}{(4-b)(4+b)} = -\frac{1}{4+b}\) 10) \(\frac{a^2-49}{49-14a+a^2} = \frac{(a-7)(a+7)}{(a-7)^2} = \frac{a+7}{a-7}\) 11) \(\frac{ax^2-2x^2-ay^2+2y^2}{ax+ay-2x-2y} = \frac{a(x^2-y^2)-2(x^2-y^2)}{a(x+y)-2(x+y)} = \frac{(a-2)(x^2-y^2)}{(a-2)(x+y)} = \frac{(x-y)(x+y)}{(x+y)} = x-y\)