Solve 1+15/2/frac{1{1}-frac{sqrt{3}}{2}}

$$\frac { 1 + \frac { 15 } { 2 } } { \frac { 1 } { 1 } - \frac { \sqrt { 3 } } { 2 } }$$

Evaluate

$$17\left(\sqrt{3}+2\right)\approx 63.444863729$$

Short Solution Steps

Divide 1 by 1 to get 1.

$$\frac{1+\frac{15}{2}}{1-\frac{\sqrt{3}}{2}}$$

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

$$\frac{\frac{2}{2}+\frac{15}{2}}{1-\frac{\sqrt{3}}{2}}$$

Since \frac{2}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+15}{2}}{1-\frac{\sqrt{3}}{2}}$$

Add 2 and 15 to get 17.

$$\frac{\frac{17}{2}}{1-\frac{\sqrt{3}}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{\frac{17}{2}}{\frac{2}{2}-\frac{\sqrt{3}}{2}}$$

Since \frac{2}{2} and \frac{\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17}{2}}{\frac{2-\sqrt{3}}{2}}$$

Divide \frac{17}{2} by \frac{2-\sqrt{3}}{2} by multiplying \frac{17}{2} by the reciprocal of \frac{2-\sqrt{3}}{2}.

$$\frac{17\times 2}{2\left(2-\sqrt{3}\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{17}{-\sqrt{3}+2}$$

Rationalize the denominator of \frac{17}{-\sqrt{3}+2} by multiplying numerator and denominator by -\sqrt{3}-2.

$$\frac{17\left(-\sqrt{3}-2\right)}{\left(-\sqrt{3}+2\right)\left(-\sqrt{3}-2\right)}$$

Consider \left(-\sqrt{3}+2\right)\left(-\sqrt{3}-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{17\left(-\sqrt{3}-2\right)}{\left(-\sqrt{3}\right)^{2}-2^{2}}$$

Expand \left(-\sqrt{3}\right)^{2}.

$$\frac{17\left(-\sqrt{3}-2\right)}{\left(-1\right)^{2}\left(\sqrt{3}\right)^{2}-2^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{17\left(-\sqrt{3}-2\right)}{1\left(\sqrt{3}\right)^{2}-2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{17\left(-\sqrt{3}-2\right)}{1\times 3-2^{2}}$$

Multiply 1 and 3 to get 3.

$$\frac{17\left(-\sqrt{3}-2\right)}{3-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{17\left(-\sqrt{3}-2\right)}{3-4}$$

Subtract 4 from 3 to get -1.

$$\frac{17\left(-\sqrt{3}-2\right)}{-1}$$

Anything divided by -1 gives its opposite.

$$-17\left(-\sqrt{3}-2\right)$$

Use the distributive property to multiply -17 by -\sqrt{3}-2.

$$17\sqrt{3}+34$$

Factor

$$17 {(\sqrt{3} + 2)} = 63.444863729$$