Solve {left(1-frac{1/2right)}^2}{3/4}+1/5/{left(1-frac{4{5}right)}^2}=frac{16}{3}

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

Verify

Solution Steps

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

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

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

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

Divide \frac{1}{4} by \frac{3}{4} by multiplying \frac{1}{4} by the reciprocal of \frac{3}{4}.

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

Multiply \frac{1}{4} and \frac{4}{3} to get \frac{1}{3}.

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

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

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

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

$$\frac{1}{3}+\frac{\frac{1}{5}}{\frac{1}{25}}=\frac{16}{3}$$

Divide \frac{1}{5} by \frac{1}{25} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{25}.

$$\frac{1}{3}+\frac{1}{5}\times 25=\frac{16}{3}$$

Multiply \frac{1}{5} and 25 to get 5.

$$\frac{1}{3}+5=\frac{16}{3}$$

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

$$\frac{16}{3}=\frac{16}{3}$$

Compare \frac{16}{3} and \frac{16}{3}.

$$\text{true}$$