Solve 2sqrt{3}-2+frac{sqrt{3}+1}{2}-1

$$2 \sqrt { 3 } - 2 + \frac { \sqrt { 3 } + 1 } { 2 } - 1$$

Evaluate

$$\frac{5\left(\sqrt{3}-1\right)}{2}\approx 1.830127019$$

Short Solution Steps

Subtract 1 from -2 to get -3.

$$2\sqrt{3}-3+\frac{\sqrt{3}+1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{3}-3 times \frac{2}{2}.

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

Since \frac{2\left(2\sqrt{3}-3\right)}{2} and \frac{\sqrt{3}+1}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(2\sqrt{3}-3\right)+\sqrt{3}+1.

$$\frac{4\sqrt{3}-6+\sqrt{3}+1}{2}$$

Do the calculations in 4\sqrt{3}-6+\sqrt{3}+1.

$$\frac{5\sqrt{3}-5}{2}$$

Factor

$$\frac{5 {(\sqrt{3} - 1)}}{2} = 1.830127018922193$$