Resolver 1/2+1/7/frac{1{2}-1/7}left(frac{2}{3}+frac{21}{24}right)9^-2

$$\frac{ \frac{ 1 }{ 2 } + \frac{ 1 }{ 7 } }{ \frac{ 1 }{ 2 } - \frac{ 1 }{ 7 } } \left( \frac{ 2 }{ 3 } + \frac{ 21 }{ 24 } \right) { 9 }^{ -2 }$$

Avaliar

$$\frac{37}{1080}\approx 0,034259259$$

Passos Para a Resolução

Some \frac{1}{2} e \frac{1}{7} para obter \frac{9}{14}.

$$\frac{\frac{9}{14}}{\frac{1}{2}-\frac{1}{7}}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Subtraia \frac{1}{7} de \frac{1}{2} para obter \frac{5}{14}.

$$\frac{\frac{9}{14}}{\frac{5}{14}}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Divida \frac{9}{14} por \frac{5}{14} ao multiplicar \frac{9}{14} pelo recíproco de \frac{5}{14}.

$$\frac{9}{14}\times \frac{14}{5}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Multiplique \frac{9}{14} e \frac{14}{5} para obter \frac{9}{5}.

$$\frac{9}{5}\left(\frac{2}{3}+\frac{21}{24}\right)\times 9^{-2}$$

Reduza a fração \frac{21}{24} para os termos mais baixos ao retirar e anular 3.

$$\frac{9}{5}\left(\frac{2}{3}+\frac{7}{8}\right)\times 9^{-2}$$

Some \frac{2}{3} e \frac{7}{8} para obter \frac{37}{24}.

$$\frac{9}{5}\times \frac{37}{24}\times 9^{-2}$$

Multiplique \frac{9}{5} e \frac{37}{24} para obter \frac{111}{40}.

$$\frac{111}{40}\times 9^{-2}$$

Calcule 9 elevado a -2 e obtenha \frac{1}{81}.

$$\frac{111}{40}\times \frac{1}{81}$$

Multiplique \frac{111}{40} e \frac{1}{81} para obter \frac{37}{1080}.

$$\frac{37}{1080}$$

Fatorizar

$$\frac{37}{2 ^ {3} \cdot 3 ^ {3} \cdot 5} = 0,03425925925925926$$