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

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

Evaluate

$$\frac{391}{36}\approx 10.861111111$$

Solution Steps

Divide \frac{4}{3} by \frac{1}{2} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{2}.

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

Multiply \frac{4}{3} and 2 to get \frac{8}{3}.

$$\left(\frac{2}{3}+\frac{8}{3}\right)^{2}-\frac{1}{4}$$

Add \frac{2}{3} and \frac{8}{3} to get \frac{10}{3}.

$$\left(\frac{10}{3}\right)^{2}-\frac{1}{4}$$

Calculate \frac{10}{3} to the power of 2 and get \frac{100}{9}.

$$\frac{100}{9}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{100}{9} to get \frac{391}{36}.

$$\frac{391}{36}$$

Factor

$$\frac{17 \cdot 23}{2 ^ {2} \cdot 3 ^ {2}} = 10\frac{31}{36} = 10.86111111111111$$