Задание 519

Решение:

• \({\largeа)}\ \frac{2^{\backslash{x}}}{x^2\phantom{^{\backslash{x}}}}-\frac{3^{\backslash1}}{x^3\phantom{^{\backslash1}}}=\frac{2\cdot{x}}{x^2\cdot{x}}-\frac{3\cdot1}{x^3\cdot1}=\frac{2x}{x^3}-\frac{3}{x^3}=\frac{2x-3}{x^3}\)

• \({\largeб)}\ \frac{7^{\backslash1}}{m^4\phantom{^{\backslash1}}}-\frac{3a^{\backslash{m^2}}}{m^2\phantom{^{\backslash{m^2}}}}=\frac{7\cdot1}{m^4\cdot1}-\frac{3a\cdot{m^2}}{m^2\cdot{m^2}}=\frac{7}{m^4}-\frac{3am^2}{m^4}=\frac{7-3am^2}{m^4}\)

• \({\largeв)}\ \frac{1^{\backslash{b^4}}}{a^5b^3\phantom{^{\backslash{b^4}}}}+\frac{1^{\backslash{a^4}}}{ab^7\phantom{^{\backslash{a^4}}}}=\frac{1\cdot{b^4}}{a^5b^3\cdot{b^4}}+\frac{1\cdot{a^4}}{ab^7\cdot{a^4}}=\frac{b^4}{a^5b^7}+\frac{a^4}{a^5b^7}=\frac{b^4+a^4}{a^5b^7}\)

• \({\largeг)}\ \frac{4^{\backslash{b^2}}}{x^4b^3\phantom{^{\backslash{b^2}}}}-\frac{3^{\backslash{x^2}}}{x^2b^5\phantom{^{\backslash{x^2}}}}=\frac{4\cdot{b^2}}{x^4b^3\cdot{b^2}}-\frac{3\cdot{x^2}}{x^2b^5\cdot{x^2}}=\frac{4b^2}{x^4b^5}-\frac{3x^2}{x^4b^5}=\frac{4b^2-3x^2}{x^4b^5}\)

• \({\largeд)}\ \frac{3a^{\backslash{z^4}}}{x^7y^5z\phantom{^{\backslash{z^4}}}}-\frac{3b^{\backslash{x^6y}}}{xy^4z^5\phantom{^{\backslash{x^6y}}}}=\frac{3a\cdot{z^4}}{x^7y^5z\cdot{z^4}}-\frac{3b\cdot{x^6y}}{xy^4z^5\cdot{x^6y}}=\frac{3az^4}{x^7y^5z^5}-\frac{3bx^6y}{x^7y^5z^5}=\frac{3az^4-3bx^6y}{x^7y^5z^5}\)

• \({\largeе)}\ \frac{m^7n^{\backslash{b^3}}}{a^4b^3c^9\phantom{^{\backslash{b^3}}}}+\frac{3mn^{2\backslash{ac^5}}}{a^3b^6c^4\phantom{^{\backslash{ac^5}}}}=\frac{m^7n\cdot{b^3}}{a^4b^3c^9\cdot{b^3}}+\frac{3mn^2\cdot{ac^5}}{a^3b^6c^4\cdot{ac^5}}=\frac{b^3m^7n}{a^4b^6c^9}+\frac{3ac^5mn^2}{a^4b^6c^9}=\frac{b^3m^7n+3ac^5mn^2}{a^4b^6c^9}\)