Math Problem Solver

\[\frac{{\left( \frac{{0.9}^{2}}{34} + \frac{{1.1}^{2}}{34} \right)}^{2}}{\frac{1}{33} \cdot {\left( \frac{{0.9}^{2}}{34} \right)}^{2} + \frac{1}{33} \cdot {\left( \frac{{1.1}^{2}}{34} \right)}^{2}} = \frac{673266}{10601} \approx 63.50966889916045656070182058296387\]

\[\begin{aligned}\frac{{\left( \frac{{0.9}^{2}}{34} + \frac{{1.1}^{2}}{34} \right)}^{2}}{\frac{1}{33} \cdot {\left( \frac{{0.9}^{2}}{34} \right)}^{2} + \frac{1}{33} \cdot {\left( \frac{{1.1}^{2}}{34} \right)}^{2}}& = \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{81}{100} \cdot \frac{1}{34} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{81}{3400} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{81}{3400} + \left(\frac{11}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{81}{3400} + \frac{121}{100} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{81}{3400} + \frac{121}{3400}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \left(\frac{101}{1700}\right)^{2} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{1}{33} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{1}{33} \cdot \left(\frac{81}{100} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{1}{33} \cdot \left(\frac{81}{3400}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{1}{33} \cdot \frac{6561}{11560000} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1}{33} \cdot \left(\left(\frac{11}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1}{33} \cdot \left(\frac{121}{100} \cdot \frac{1}{34}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1}{33} \cdot \left(\frac{121}{3400}\right)^{2}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1}{33} \cdot \frac{14641}{11560000}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{2187}{127160000} + \frac{1331}{34680000}}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{10601}{190740000}}\\& = \frac{673266}{10601}\end{aligned}\]