Solve 1-(1/6-1/3)/(frac{1{6}+1/2)^2+frac{3}{2}}é

$$\frac { 1 - ( \frac { 1 } { 6 } - \frac { 1 } { 3 } ) } { ( \frac { 1 } { 6 } + \frac { 1 } { 2 } ) ^ { 2 } + \frac { 3 } { 2 } } é$$

Evaluate

$$\frac{3é}{5}$$

Solution Steps

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

$$\frac{1-\left(-\frac{1}{6}\right)}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$\frac{1+\frac{1}{6}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$\frac{\frac{7}{6}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

Add \frac{1}{6} and \frac{1}{2} to get \frac{2}{3}.

$$\frac{\frac{7}{6}}{\left(\frac{2}{3}\right)^{2}+\frac{3}{2}}é$$

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

$$\frac{\frac{7}{6}}{\frac{4}{9}+\frac{3}{2}}é$$

Add \frac{4}{9} and \frac{3}{2} to get \frac{35}{18}.

$$\frac{\frac{7}{6}}{\frac{35}{18}}é$$

Divide \frac{7}{6} by \frac{35}{18} by multiplying \frac{7}{6} by the reciprocal of \frac{35}{18}.

$$\frac{7}{6}\times \frac{18}{35}é$$

Multiply \frac{7}{6} and \frac{18}{35} to get \frac{3}{5}.

$$\frac{3}{5}é$$

Expand

$$\frac{3é}{5}$$

Solution Steps

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

$$\frac{1-\left(-\frac{1}{6}\right)}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$\frac{1+\frac{1}{6}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$\frac{\frac{7}{6}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}é$$

Add \frac{1}{6} and \frac{1}{2} to get \frac{2}{3}.

$$\frac{\frac{7}{6}}{\left(\frac{2}{3}\right)^{2}+\frac{3}{2}}é$$

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

$$\frac{\frac{7}{6}}{\frac{4}{9}+\frac{3}{2}}é$$

Add \frac{4}{9} and \frac{3}{2} to get \frac{35}{18}.

$$\frac{\frac{7}{6}}{\frac{35}{18}}é$$

Divide \frac{7}{6} by \frac{35}{18} by multiplying \frac{7}{6} by the reciprocal of \frac{35}{18}.

$$\frac{7}{6}\times \frac{18}{35}é$$

Multiply \frac{7}{6} and \frac{18}{35} to get \frac{3}{5}.

$$\frac{3}{5}é$$