Question

Выполните сложение или вычитание дробей: 1) а) х/3+х-2/5 б)3у-2/6-у+1/4 в) -bc/7+3b-c/14 г)1/а^2+а-2/а д)3х-5/х-3у-2/у е)b-a/ab-a-b/b^2

Answer 1

$\frac{x}{3}+\frac{x-2}{5}=\frac{5x+3(x-2)}{15} =\frac{5x+3x-6}{15} =\frac{8x-6}{15}\\ \\$$\\ \\ \frac{3y-2}{6} -\frac{y+1}{4} =\frac{2(3y-2)-3(y+1)}{12} =\frac{6y-4-3y-3}{12} =\frac{3y-7}{12} \\ \\- \frac{bc}{7} +\frac{3b-c}{14} =\frac{-2bc+3b-c}{14} \\ \\ \frac{1}{a^{2} } +\frac{a-2}{a} =\frac{1+a(a-2)}{a^{2} } =\frac{1+a^{2}-2a }{a^{2} } =\frac{a^{2}-2a+1 }{a^{2} } =\frac{(a+1)^{2}}{a^{2} } \\ \\ \frac{3x-5}{x} -\frac{3y-2}{y}=\frac{y(3x-5)-x(3y-2)}{xy}=\frac{3xy-5y-3xy+2x}{xy}=\frac{2x-5y}{xy} \\ \\$$\frac{b-a}{ab} -\frac{a-b}{b^{2} }=\frac{b(b-a)-a(a-b)}{ab^{2} }=\frac{b^{2}-ab-a^{2}+ab}{ab^{2}}=\frac{b^{2}- a^{2} }{ab^{2}}=\frac{(b-a)(b+a)}{ab^{2}}$