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

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

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Subtract \frac{1}{2} from \frac{3}{4} to get \frac{1}{4}.

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

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(-\frac{5}{4}+2\right)^{2}}+\left(\frac{5}{4}-1\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Add -\frac{5}{4} and 2 to get \frac{3}{4}.

$$\frac{\frac{1}{16}}{\left(\frac{3}{4}\right)^{2}}+\left(\frac{5}{4}-1\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\frac{1}{16}}{\frac{9}{16}}+\left(\frac{5}{4}-1\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Divide \frac{1}{16} by \frac{9}{16} by multiplying \frac{1}{16} by the reciprocal of \frac{9}{16}.

$$\frac{1}{16}\times \frac{16}{9}+\left(\frac{5}{4}-1\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Multiply \frac{1}{16} and \frac{16}{9} to get \frac{1}{9}.

$$\frac{1}{9}+\left(\frac{5}{4}-1\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Subtract 1 from \frac{5}{4} to get \frac{1}{4}.

$$\frac{1}{9}+\left(\frac{1}{4}\right)^{2}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{9}+\frac{1}{16}\left(\frac{1}{3}+5\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Add \frac{1}{3} and 5 to get \frac{16}{3}.

$$\frac{1}{9}+\frac{1}{16}\times \left(\frac{16}{3}\right)^{2}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Calculate \frac{16}{3} to the power of 2 and get \frac{256}{9}.

$$\frac{1}{9}+\frac{1}{16}\times \frac{256}{9}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Multiply \frac{1}{16} and \frac{256}{9} to get \frac{16}{9}.

$$\frac{1}{9}+\frac{16}{9}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Add \frac{1}{9} and \frac{16}{9} to get \frac{17}{9}.

$$\frac{17}{9}-\frac{4-\frac{4}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Subtract \frac{4}{5} from 4 to get \frac{16}{5}.

$$\frac{17}{9}-\frac{\frac{16}{5}}{\left(-2+\frac{4}{5}\right)^{2}}+1$$

Add -2 and \frac{4}{5} to get -\frac{6}{5}.

$$\frac{17}{9}-\frac{\frac{16}{5}}{\left(-\frac{6}{5}\right)^{2}}+1$$

Calculate -\frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\frac{17}{9}-\frac{\frac{16}{5}}{\frac{36}{25}}+1$$

Divide \frac{16}{5} by \frac{36}{25} by multiplying \frac{16}{5} by the reciprocal of \frac{36}{25}.

$$\frac{17}{9}-\frac{16}{5}\times \frac{25}{36}+1$$

Multiply \frac{16}{5} and \frac{25}{36} to get \frac{20}{9}.

$$\frac{17}{9}-\frac{20}{9}+1$$

Subtract \frac{20}{9} from \frac{17}{9} to get -\frac{1}{3}.

$$-\frac{1}{3}+1$$

Add -\frac{1}{3} and 1 to get \frac{2}{3}.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$