Solve (1/2+1/3+1/6/frac{1{2}+frac{2}{3}})^2+frac{13}{49}

$$( \frac { \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 6 } } { \frac { 1 } { 2 } + \frac { 2 } { 3 } } ) ^ { 2 } + \frac { 13 } { 49 }$$

Evaluate

$$1$$

Solution Steps

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$\left(\frac{\frac{5}{6}+\frac{1}{6}}{\frac{1}{2}+\frac{2}{3}}\right)^{2}+\frac{13}{49}$$

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

$$\left(\frac{1}{\frac{1}{2}+\frac{2}{3}}\right)^{2}+\frac{13}{49}$$

Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\left(\frac{1}{\frac{7}{6}}\right)^{2}+\frac{13}{49}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$\left(1\times \frac{6}{7}\right)^{2}+\frac{13}{49}$$

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

$$\left(\frac{6}{7}\right)^{2}+\frac{13}{49}$$

Calculate \frac{6}{7} to the power of 2 and get \frac{36}{49}.

$$\frac{36}{49}+\frac{13}{49}$$

Add \frac{36}{49} and \frac{13}{49} to get 1.

$$1$$

Factor

$$1$$