Solve a_{2}:3/2/frac{1{2}+3}

$$a _ { 2 } : \frac { \frac { 3 } { 2 } } { \frac { 1 } { 2 } + 3 }$$

Evaluate

$$\frac{7a_{2}}{3}$$

Solution Steps

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

$$\frac{a_{2}\left(\frac{1}{2}+3\right)}{\frac{3}{2}}$$

Convert 3 to fraction \frac{6}{2}.

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

Since \frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{a_{2}\times \frac{1+6}{2}}{\frac{3}{2}}$$

Add 1 and 6 to get 7.

$$\frac{a_{2}\times \frac{7}{2}}{\frac{3}{2}}$$

Divide a_{2}\times \frac{7}{2} by \frac{3}{2} by multiplying a_{2}\times \frac{7}{2} by the reciprocal of \frac{3}{2}.

$$\frac{a_{2}\times \frac{7}{2}\times 2}{3}$$

Cancel out 2 and 2.

$$\frac{a_{2}\times 7}{3}$$

Differentiate w.r.t. a_2

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$