Задание 516

Решение:

• \({\largeа)}\ \frac{x^{\backslash1}}{8\phantom{^{\backslash1}}}-\frac{x^{\backslash2}}{4\phantom{^{\backslash2}}}=\frac{x\cdot1}{8\cdot1}-\frac{x\cdot2}{4\cdot2}=\frac{x}{8}-\frac{2x}{8}=\frac{x-2x}{8}=\frac{{-}x}{8}={-}\frac{x}{8}\)

• \({\largeб)}\ \frac{a^{\backslash4}}{6\phantom{^{\backslash4}}}+\frac{a^{\backslash3}}{8\phantom{^{\backslash3}}}=\frac{a\cdot4}{6\cdot4}+\frac{a\cdot3}{8\cdot3}=\frac{4a}{24}+\frac{3a}{24}=\frac{4a+3a}{24}=\frac{7a}{24}\)

• \({\largeв)}\ \frac{m^{2\backslash2}}{3\phantom{^{\backslash2}}}-\frac{2m^{\backslash3}}{2\phantom{^{\backslash3}}}=\frac{m^2\cdot2}{3\cdot2}-\frac{2m\cdot3}{2\cdot3}=\frac{2m^2}{6}-\frac{6m}{6}=\frac{2m^2-6m}{6}=\frac{ 2(m^2-3m)}{6}=\frac{m^2-3m}{3}\)

• \({\largeг)}\ \frac{a-1^{\backslash3}}{10\phantom{^{\backslash3}}}+\frac{a^{\backslash2}}{15\phantom{^{\backslash2}}}=\frac{ (a-1)\cdot3}{10\cdot3}+\frac{a\cdot2}{15\cdot2}=\frac{3a-3}{30}+\frac{2a}{30}=\frac{3a-3+2a}{30}=\frac{5a-3}{30}\)

• \({\largeд)}\ \frac{2x+3^{\backslash4}}{6\phantom{^{\backslash4}}}+\frac{x-1^{\backslash3}}{8\phantom{^{\backslash3}}}=\frac{ (2x+3)\cdot4}{6\cdot4}+\frac{ (x-1)\cdot3}{8\cdot3}=\frac{8x+12}{24}+\frac{3x-3}{24}=\frac{8x+12+3x-3}{24}=\frac{11x+9}{24}\)

• \({\largeе)}\ \frac{a-3^{\backslash3}}{10\phantom{^{\backslash3}}}-\frac{2-a^{\backslash2}}{15\phantom{^{\backslash2}}}=\frac{ (a-3)\cdot3}{10\cdot3}-\frac{ (2-a)\cdot2}{15\cdot2}=\frac{3a-9}{30}-\frac{4-2a}{30}=\frac{ 3a-9-(4-2a)}{30}=\frac{3a-9-4+2a}{30}=\frac{5a-13}{30}\)