Задание 517

Решение:

• \({\largeа)}\ \frac{1^{\backslash3}}{4x\phantom{^{\backslash3}}}-\frac{1^{\backslash4}}{3x\phantom{^{\backslash4}}}=\frac{1\cdot3}{4x\cdot3}-\frac{1\cdot4}{3x\cdot4}=\frac{3}{12x}-\frac{4}{12x}=\frac{3-4}{12x}=\frac{{-}1}{12x}={-}\frac{1}{12x}\)

• \({\largeб)}\ \frac{1^{\backslash4}}{m\phantom{^{\backslash4}}}+\frac{5^{\backslash1}}{4m\phantom{^{\backslash1}}}=\frac{1\cdot4}{m\cdot4}+\frac{5\cdot1}{4m\cdot1}=\frac{4}{4m}+\frac{5}{4m}=\frac{4+5}{4m}=\frac{9}{4m}\)

• \({\largeв)}\ \frac{2^{\backslash{q}}}{p\phantom{^{\backslash{q}}}}+\frac{3^{\backslash1}}{pq\phantom{^{\backslash1}}}=\frac{2\cdot{q}}{p\cdot{q}}+\frac{3\cdot1}{pq\cdot1}=\frac{2q}{pq}+\frac{3}{pq}=\frac{2q+3}{pq}\)

• \({\largeг)}\ \frac{a^{\backslash1}}{xy\phantom{^{\backslash1}}}-\frac{b^{\backslash{y}}}{x\phantom{^{\backslash{y}}}}=\frac{a\cdot1}{xy\cdot1}-\frac{b\cdot{y}}{x\cdot{y}}=\frac{a}{xy}-\frac{by}{xy}=\frac{a-by}{xy}\)

• \({\largeд)}\ \frac{m^{\backslash{m}}}{n^2\phantom{^{\backslash{m}}}}-\frac{1^{\backslash{n}}}{mn\phantom{^{\backslash{n}}}}=\frac{m\cdot{m}}{n^2\cdot{m}}-\frac{1\cdot{n}}{mn\cdot{n}}=\frac{m^2}{mn^2}-\frac{n}{mn^2}=\frac{m^2-n}{mn^2}\)

• \({\largeе)}\ \frac{a^{\backslash2a}}{3b^2\phantom{^{\backslash2a}}}+\frac{8^{\backslash3b}}{2ab\phantom{^{\backslash3b}}}=\frac{a\cdot2a}{3b^2\cdot2a}+\frac{8\cdot3b}{2ab\cdot3b}=\frac{2a^2}{6ab^2}+\frac{24b}{6ab^2}=\frac{2a^2+24b}{6ab^2}=\frac{ 2(a^2+12b)}{6ab^2}=\frac{a^2+12b}{3ab^2}\)