Solve frac{sqrt{3}}{2}+5-1/2x12*5div13*6

$$\frac { \sqrt { 3 } } { 2 } + 5 - \frac { 1 } { 2 } x 12 \cdot 5 \div 13 \cdot 6$$

Evaluate

$$-\frac{15x_{12}}{13}+\frac{\sqrt{3}}{2}+5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\frac{\sqrt{3}}{2}+\frac{5\times 2}{2}-\frac{\frac{1}{2}x_{12}\times 5}{13}\times 6$$

Since \frac{\sqrt{3}}{2} and \frac{5\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{3}+5\times 2}{2}-\frac{\frac{1}{2}x_{12}\times 5}{13}\times 6$$

Do the multiplications in \sqrt{3}+5\times 2.

$$\frac{\sqrt{3}+10}{2}-\frac{\frac{1}{2}x_{12}\times 5}{13}\times 6$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\frac{\sqrt{3}+10}{2}-\frac{\frac{5}{2}x_{12}}{13}\times 6$$

Divide \frac{5}{2}x_{12} by 13 to get \frac{5}{26}x_{12}.

$$\frac{\sqrt{3}+10}{2}-\frac{5}{26}x_{12}\times 6$$

Express \frac{5}{26}\times 6 as a single fraction.

$$\frac{\sqrt{3}+10}{2}-\frac{5\times 6}{26}x_{12}$$

Multiply 5 and 6 to get 30.

$$\frac{\sqrt{3}+10}{2}-\frac{30}{26}x_{12}$$

Reduce the fraction \frac{30}{26} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{3}+10}{2}-\frac{15}{13}x_{12}$$

Factor

$$\frac{-30x_{12}+13\sqrt{3}+130}{26}$$

Solution Steps

Factor out \frac{1}{26}.

$$\frac{13\sqrt{3}+130-30x_{12}}{26}$$