Представьте в виде дроби

**75. Представьте в виде дроби:** а) $$\frac{x}{2} + \frac{y}{3} = \frac{3x}{6} + \frac{2y}{6} = \frac{3x+2y}{6}$$ б) $$\frac{c}{4} - \frac{d}{12} = \frac{3c}{12} - \frac{d}{12} = \frac{3c-d}{12}$$ в) $$\frac{a}{b} - \frac{b^2}{a} = \frac{a^2}{ab} - \frac{b^3}{ab} = \frac{a^2-b^3}{ab}$$ г) $$\frac{2}{3x} - \frac{3}{2x} = \frac{4}{6x} - \frac{9}{6x} = \frac{4-9}{6x} = \frac{-5}{6x}$$ д) $$\frac{5x}{8y} + \frac{x}{4y} = \frac{5x}{8y} + \frac{2x}{8y} = \frac{5x+2x}{8y} = \frac{7x}{8y}$$ е) $$\frac{17y}{24c} - \frac{25y}{36c^2} = \frac{17y \cdot 3c}{72c^2} - \frac{25y \cdot 2}{72c^2} = \frac{51cy - 50y}{72c^2} = \frac{y(51c-50)}{72c^2}$$ ж) $$\frac{1}{5a} - \frac{8}{25a^2} = \frac{5a}{25a^2} - \frac{8}{25a^2} = \frac{5a-8}{25a^2}$$ з) $$\frac{3b}{4c} + \frac{c}{4b} = \frac{3b \cdot b}{4bc} + \frac{c \cdot c}{4bc} = \frac{3b^2+c^2}{4bc}$$ **76. Выполните действия:** а) $$\frac{5y-3}{6y} + \frac{y+2}{4y} = \frac{2(5y-3)}{12y} + \frac{3(y+2)}{12y} = \frac{10y-6+3y+6}{12y} = \frac{13y}{12y} = \frac{13}{12}$$ б) $$\frac{3x+5}{36x} + \frac{x-3}{21x} = \frac{7(3x+5)}{252x} + \frac{12(x-3)}{252x} = \frac{21x+35+12x-36}{252x} = \frac{33x-1}{252x}$$ в) $$\frac{b+2}{15b} - \frac{3c-5}{45c} = \frac{3c(b+2)}{45bc} - \frac{b(3c-5)}{45bc} = \frac{3bc+6c-3bc+5b}{45bc} = \frac{6c+5b}{45bc}$$ г) $$\frac{8b+y}{40b} - \frac{6y+b}{30y} = \frac{3y(8b+y)}{120by} - \frac{4b(6y+b)}{120by} = \frac{24by+3y^2-24by-4b^2}{120by} = \frac{3y^2-4b^2}{120by}$$ **77. Преобразуйте в дробь выражение:** а) $$\frac{15a-b}{12a} - \frac{a-4b}{9a} = \frac{3(15a-b)}{36a} - \frac{4(a-4b)}{36a} = \frac{45a-3b-4a+16b}{36a} = \frac{41a+13b}{36a}$$ б) $$\frac{7x+4}{8y} - \frac{3x-1}{6y} = \frac{3(7x+4)}{24y} - \frac{4(3x-1)}{24y} = \frac{21x+12-12x+4}{24y} = \frac{9x+16}{24y}$$ **78. Выполните действие:** а) $$\frac{b}{a^2} - \frac{1}{a} = \frac{b}{a^2} - \frac{a}{a^2} = \frac{b-a}{a^2}$$ б) $$\frac{1}{2a} + \frac{4-2a^2}{a^{10}} = \frac{a^9}{2a^{10}} + \frac{2(4-2a^2)}{2a^{10}} = \frac{a^9+8-4a^2}{2a^{10}}$$ в) $$\frac{a+b}{a^2} + \frac{a-b}{ab} = \frac{b(a+b)}{a^2b} + \frac{a(a-b)}{a^2b} = \frac{ab+b^2+a^2-ab}{a^2b} = \frac{a^2+b^2}{a^2b}$$ г) $$\frac{2a-3b}{a^2b} - \frac{4a-5b}{ab^2} = \frac{b(2a-3b)}{a^2b^2} - \frac{a(4a-5b)}{a^2b^2} = \frac{2ab-3b^2-4a^2+5ab}{a^2b^2} = \frac{7ab-3b^2-4a^2}{a^2b^2}$$ д) $$\frac{x-2y}{xy^2} + \frac{2y-x}{x^2y} = \frac{x(x-2y)}{x^2y^2} + \frac{y(2y-x)}{x^2y^2} = \frac{x^2-2xy+2y^2-xy}{x^2y^2} = \frac{x^2-3xy+2y^2}{x^2y^2}$$ **79. Представьте в виде дроби:** а) $$\frac{2xy-1}{3y} - \frac{2x-y}{3x} = \frac{x(2xy-1)}{3xy} - \frac{y(2x-y)}{3xy} = \frac{2x^2y-x-2xy+y^2}{3xy} = \frac{2x^2y-x-2xy+y^2}{3xy}$$ б) $$\frac{1}{3a^2} - \frac{2}{5a^3} = \frac{5a}{15a^3} - \frac{6}{15a^3} = \frac{5a-6}{15a^3}$$