Упражнение 110

\(1)\ \frac{a}{b}+1={\frac{a}{b}}^{\backslash1}+{\frac{1}{1}}^{\backslash{b}}=\frac{a+b}{b};\)

\(2)\ \frac{x}{y}-x={\frac{x}{y}}^{\backslash1}-{\frac{x}{1}}^{\backslash{y}}=\frac{x-xy}{y};\)

\(3)\ \frac{m}{n}+\frac{n}{m}+2={\frac{m}{n}}^{\backslash{m}}+{\frac{n}{m}}^{\backslash{n}}+{\frac{2}{1}}^{\backslash{mn}}=\frac{m^2+n^2+2mn}{mn}=\frac{m^2+2mn+n^2}{mn};\)

\(4)\ \frac{9}{p^2}-\frac{4}{p}+3={\frac{9}{p^2}}^{\backslash1}-{\frac{4}{p}}^{\backslash{p}}+{\frac{3}{1}}^{\backslash{p^2}}=\frac{9-4p+3p^2}{p^2}=\frac{3p^2-4p+9}{p^2};\)

\(5)\ 2-\frac{3b+2a}{a}={\frac{2}{1}}^{\backslash{a}}-{\frac{3b+2a}{a}}^{\backslash1}=\frac{2a-(3b+2a)}{a}=\frac{2a-3b-2a}{a}=\frac{{-}3b}{a}={-}\frac{3b}{a};\)

\(6)\ \frac{3b+4}{b-2}-3={\frac{3b+4}{b-2}}^{\backslash1}-{\frac{3}{1}}^{\backslash{b\ -\ 2}}=\frac{3b+4-3(b-2)}{b-2}=\frac{3b+4-3b+6}{b-2}=\frac{10}{b-2};\)

\(7)\ 6m-\frac{12m^2+1}{2m}={\frac{6m}{1}}^{\backslash2m}-{\frac{12m^2+1}{2m}}^{\backslash1}=\frac{12m^2-(12m^2+1)}{2m}=\frac{12m^2-12m^2-1}{2m}=\frac{{-}1}{2m}={-}\frac{1}{2m};\)

\(8)\ \frac{20b^2+5}{2b-1}-10b={\frac{20b^2+5}{2b-1}}^{\backslash1}-{\frac{10b}{1}}^{\backslash{2b\ -\ 1}}=\frac{20b^2+5-10b(2b-1)}{2b-1}=\frac{20b^2+5-20b^2+10b}{2b-1}=\frac{10b+5}{2b-1}.\)