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

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

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

Multiply 2 and 1 to get 2.

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

Convert 2 to fraction \frac{4}{2}.

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

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 4 to get 3.

$$\frac{\frac{3}{2}}{\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{1}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{3}{2}}{\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{\sqrt{3}}{1}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{3}{2}}{\frac{\sqrt{3}}{3}\times \frac{\sqrt{3}}{1}}$$

Anything divided by one gives itself.

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

Express \frac{\sqrt{3}}{3}\sqrt{3} as a single fraction.

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

Divide \frac{3}{2} by \frac{\sqrt{3}\sqrt{3}}{3} by multiplying \frac{3}{2} by the reciprocal of \frac{\sqrt{3}\sqrt{3}}{3}.

$$\frac{3\times 3}{2\sqrt{3}\sqrt{3}}$$

Rationalize the denominator of \frac{3\times 3}{2\sqrt{3}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3\times 3\sqrt{3}}{2\left(\sqrt{3}\right)^{2}\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$\frac{3\times 3\sqrt{3}}{2\times 3\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

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

Multiply 3 and 3 to get 9.

$$\frac{9}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$