Answer:
[tex](\frac{3^{-1}+2^{-1}}{5^{-1}})^{-1}+3=\frac{81}{25}[/tex]
Step-by-step explanation:
Given expression is,
[tex](\frac{3^{-1}+2^{-1}}{5^{-1}})^{-1}+3[/tex]
By solving the given expression,
[tex](\frac{3^{-1}+2^{-1}}{5^{-1}})^{-1}+3=(\frac{\frac{1}{3}+\frac{1}{2}}{\frac{1}{5}})^{-1}+3[/tex]
[tex]=(\frac{\frac{2+3}{6}}{\frac{1}{5}})^{-1}+3[/tex]
[tex]=(\frac{\frac{5}{6}}{\frac{1}{5}})^{-1}+3[/tex]
[tex]=(\frac{5}{6}\times \frac{5}{1})^{-1}+3[/tex]
[tex]=(\frac{25}{6})^{-1}+3[/tex]
[tex]=\frac{6}{25}+3[/tex]
[tex]=\frac{6+(25\times 3)}{25}[/tex]
[tex]=\frac{81}{25}[/tex]
