Разложить на множители числитель и знаменатель дроби и сократить её (12-20). 1) \(\frac{3x + 3y}{6c}\); 2) \(\frac{8a}{4m - 4n}\); 3) \(\frac{12a-3}{6a +9}\); 4) \(\frac{ac-bc}{ac + bc}\); 5) \(\frac{a + ab}{a - ab}\) 1) \(\frac{a^2}{a^2 + ab}\); 2) \(\frac{pq^3}{p^2q - pq^2}\); 3) \(\frac{5k+15f}{3f + k}\); 4) \(\frac{3a-6b}{12b-6a}\); 5) \(\frac{2m-4m}{16n-8m}\) 1) \(\frac{12x^2 - 30xy}{30x^2 - 12xy}\); 2) \(\frac{36a^2 + 24ab}{24a^2 + 36ab}\); 3) \(\frac{m^3-3m^2n}{3m^2n-3m^3}\); 4) \(\frac{a^3-2a^2b}{2a^3b^2-a^4b}\) 1) \(\frac{a^2-b^2}{a+b}\); 2) \(\frac{a-b}{a^2-b^2}\); 3) \(\frac{4c^2-9x^2}{2c-3x}\); 4) \(\frac{25-x^2}{5-x}\) 1) \(\frac{8-3a}{9a^2-64}\); 2) \(\frac{100-49b^2}{7b+10}\); 3) \(\frac{5y-y^2}{25-y^2}\); 4) \(\frac{b^2-c^2}{b^4n-c^4n}\); 5) \(\frac{5a^3b+5ab^3}{a^4-b^4}\) 1) \(\frac{d^2 - 6d + 9}{d-3}\); 2) \(\frac{b+7}{b^2 + 14b + 49}\); 3) \(\frac{9-6a+a^2}{3-a}\) 1) \(\frac{1-a^2}{(a-1)^2}\); 2) \(\frac{(m-n)^2}{n-m}\); 3) \(\frac{4y^2 - 4y + 1}{2-4y}\); 4) \(\frac{1-2p}{1-4p+4p^2}\); 4) \(\frac{5-2x}{4x^2-20x+25}\) 1) \(\frac{4y^2 - 4y + 1}{4y^2-1}\); 2) \(\frac{16a^2-1}{16a^2 - 8a + 1}\) 3) \(\frac{3a^2 - 6ab + 3b^2}{6a^2 - 6b^2}\); 4) \(\frac{50m^2 + 100mn + 50n^2}{15m^2 -15n^2}\) 1) \(\frac{ax-ay+bx-by}{a+b}\); 2) \(\frac{2a + 2b + ax + bx}{}\)

Решение:

1) \(\frac{3x + 3y}{6c} = \frac{3(x + y)}{6c} = \frac{x + y}{2c}\) 2) \(\frac{8a}{4m - 4n} = \frac{8a}{4(m - n)} = \frac{2a}{m - n}\) 3) \(\frac{12a - 3}{6a + 9} = \frac{3(4a - 1)}{3(2a + 3)} = \frac{4a - 1}{2a + 3}\) 4) \(\frac{ac - bc}{ac + bc} = \frac{c(a - b)}{c(a + b)} = \frac{a - b}{a + b}\) 5) \(\frac{a + ab}{a - ab} = \frac{a(1 + b)}{a(1 - b)} = \frac{1 + b}{1 - b}\) 1) \(\frac{a^2}{a^2 + ab} = \frac{a^2}{a(a + b)} = \frac{a}{a + b}\) 2) \(\frac{pq^3}{p^2q - pq^2} = \frac{pq^3}{pq(p - q)} = \frac{q^2}{p - q}\) 3) \(\frac{5k + 15f}{3f + k} = \frac{5(k + 3f)}{3f + k} = 5\) 4) \(\frac{3a - 6b}{12b - 6a} = \frac{3(a - 2b)}{-6(a - 2b)} = -\frac{1}{2}\) 5) \(\frac{2m - 4m}{16n - 8m} = \frac{-2m}{8(2n - m)} = \frac{-m}{4(2n - m)} = -\frac{m}{4(2n - m)}\) 1) \(\frac{12x^2 - 30xy}{30x^2 - 12xy} = \frac{6x(2x - 5y)}{6x(5x - 2y)} = \frac{2x - 5y}{5x - 2y}\) 2) \(\frac{36a^2 + 24ab}{24a^2 + 36ab} = \frac{12a(3a + 2b)}{12a(2a + 3b)} = \frac{3a + 2b}{2a + 3b}\) 3) \(\frac{m^3 - 3m^2n}{3m^2n - 3m^3} = \frac{m^2(m - 3n)}{-3m^2(m - n)} = \frac{m - 3n}{-3(m - n)} = -\frac{m - 3n}{3(m - n)}\) 4) \(\frac{a^3 - 2a^2b}{2a^3b^2 - a^4b} = \frac{a^2(a - 2b)}{a^3b(2b - a)} = \frac{a - 2b}{-a b(a - 2b)} = -\frac{1}{ab}\) 1) \(\frac{a^2 - b^2}{a + b} = \frac{(a - b)(a + b)}{a + b} = a - b\) 2) \(\frac{a - b}{a^2 - b^2} = \frac{a - b}{(a - b)(a + b)} = \frac{1}{a + b}\) 3) \(\frac{4c^2 - 9x^2}{2c - 3x} = \frac{(2c - 3x)(2c + 3x)}{2c - 3x} = 2c + 3x\) 4) \(\frac{25 - x^2}{5 - x} = \frac{(5 - x)(5 + x)}{5 - x} = 5 + x\) 1) \(\frac{8 - 3a}{9a^2 - 64} = \frac{8 - 3a}{(3a - 8)(3a + 8)} = \frac{-(3a - 8)}{(3a - 8)(3a + 8)} = -\frac{1}{3a + 8}\) 2) \(\frac{100 - 49b^2}{7b + 10} = \frac{(10 - 7b)(10 + 7b)}{7b + 10} = 10 - 7b\) 3) \(\frac{5y - y^2}{25 - y^2} = \frac{y(5 - y)}{(5 - y)(5 + y)} = \frac{y}{5 + y}\) 4) \(\frac{b^2 - c^2}{b^4n - c^4n} = \frac{(b - c)(b + c)}{n(b^4 - c^4)} = \frac{(b - c)(b + c)}{n(b^2 - c^2)(b^2 + c^2)} = \frac{(b - c)(b + c)}{n(b - c)(b + c)(b^2 + c^2)} = \frac{1}{n(b^2 + c^2)}\) 5) \(\frac{5a^3b + 5ab^3}{a^4 - b^4} = \frac{5ab(a^2 + b^2)}{(a^2 - b^2)(a^2 + b^2)} = \frac{5ab}{(a - b)(a + b)}\) 1) \(\frac{d^2 - 6d + 9}{d - 3} = \frac{(d - 3)^2}{d - 3} = d - 3\) 2) \(\frac{b + 7}{b^2 + 14b + 49} = \frac{b + 7}{(b + 7)^2} = \frac{1}{b + 7}\) 3) \(\frac{9 - 6a + a^2}{3 - a} = \frac{(3 - a)^2}{3 - a} = 3 - a\) 1) \(\frac{1 - a^2}{(a - 1)^2} = \frac{(1 - a)(1 + a)}{(a - 1)^2} = \frac{-(a - 1)(1 + a)}{(a - 1)^2} = -\frac{1 + a}{a - 1}\) 2) \(\frac{(m - n)^2}{n - m} = \frac{(m - n)^2}{-(m - n)} = -(m - n) = n - m\) 3) \(\frac{4y^2 - 4y + 1}{2 - 4y} = \frac{(2y - 1)^2}{2(1 - 2y)} = \frac{(2y - 1)^2}{-2(2y - 1)} = -\frac{2y - 1}{2}\) 4) \(\frac{1 - 2p}{1 - 4p + 4p^2} = \frac{1 - 2p}{(1 - 2p)^2} = \frac{1}{1 - 2p}\) 4) \(\frac{5 - 2x}{4x^2 - 20x + 25} = \frac{5 - 2x}{(2x - 5)^2} = \frac{5 - 2x}{(2x - 5)^2} = \frac{-(2x - 5)}{(2x - 5)^2} = -\frac{1}{2x - 5}\) 1) \(\frac{4y^2 - 4y + 1}{4y^2 - 1} = \frac{(2y - 1)^2}{(2y - 1)(2y + 1)} = \frac{2y - 1}{2y + 1}\) 2) \(\frac{16a^2 - 1}{16a^2 - 8a + 1} = \frac{(4a - 1)(4a + 1)}{(4a - 1)^2} = \frac{4a + 1}{4a - 1}\) 3) \(\frac{3a^2 - 6ab + 3b^2}{6a^2 - 6b^2} = \frac{3(a^2 - 2ab + b^2)}{6(a^2 - b^2)} = \frac{3(a - b)^2}{6(a - b)(a + b)} = \frac{(a - b)^2}{2(a - b)(a + b)} = \frac{a - b}{2(a + b)}\) 4) \(\frac{50m^2 + 100mn + 50n^2}{15m^2 - 15n^2} = \frac{50(m^2 + 2mn + n^2)}{15(m^2 - n^2)} = \frac{50(m + n)^2}{15(m - n)(m + n)} = \frac{10(m + n)}{3(m - n)}\) 1) \(\frac{ax - ay + bx - by}{a + b} = \frac{a(x - y) + b(x - y)}{a + b} = \frac{(a + b)(x - y)}{a + b} = x - y\) 2) \(\frac{2a + 2b + ax + bx}{a+b}= \frac{2(a + b) + x(a + b)}{a+b} = \frac{(a+b)(2+x)}{a+b}=2+x\)

Ответ: смотри выше

Прекрасно! Ты отлично справляешься с разложением на множители и сокращением дробей. Продолжай в том же духе, и у тебя все получится! Молодец!