Solve {3+3/5/1+frac{1{5}}(3/2-1/3)+sqrt{2+frac{1}{4}}}^-2

$$\{ \frac { 3 + \frac { 3 } { 5 } } { 1 + \frac { 1 } { 5 } } ( \frac { 3 } { 2 } - \frac { 1 } { 3 } ) + \sqrt { 2 + \frac { 1 } { 4 } } \} ^ { - 2 }$$

Evaluate

$$\frac{1}{25}=0.04$$

Solution Steps

Add 3 and \frac{3}{5} to get \frac{18}{5}.

$$\left(\frac{\frac{18}{5}}{1+\frac{1}{5}}\left(\frac{3}{2}-\frac{1}{3}\right)+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Add 1 and \frac{1}{5} to get \frac{6}{5}.

$$\left(\frac{\frac{18}{5}}{\frac{6}{5}}\left(\frac{3}{2}-\frac{1}{3}\right)+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Divide \frac{18}{5} by \frac{6}{5} by multiplying \frac{18}{5} by the reciprocal of \frac{6}{5}.

$$\left(\frac{18}{5}\times \frac{5}{6}\left(\frac{3}{2}-\frac{1}{3}\right)+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Multiply \frac{18}{5} and \frac{5}{6} to get 3.

$$\left(3\left(\frac{3}{2}-\frac{1}{3}\right)+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Subtract \frac{1}{3} from \frac{3}{2} to get \frac{7}{6}.

$$\left(3\times \frac{7}{6}+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Multiply 3 and \frac{7}{6} to get \frac{7}{2}.

$$\left(\frac{7}{2}+\sqrt{2+\frac{1}{4}}\right)^{-2}$$

Add 2 and \frac{1}{4} to get \frac{9}{4}.

$$\left(\frac{7}{2}+\sqrt{\frac{9}{4}}\right)^{-2}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\left(\frac{7}{2}+\frac{3}{2}\right)^{-2}$$

Add \frac{7}{2} and \frac{3}{2} to get 5.

$$5^{-2}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{1}{25}$$

Factor

$$\frac{1}{5 ^ {2}} = 0.04$$