Solve B=1/2-sqrt{3}+1/2+sqrt{3}+2014

$$B = \frac { 1 } { 2 - \sqrt { 3 } } + \frac { 1 } { 2 + \sqrt { 3 } } + 2014$$

Solve for B

$$B=2018$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{2-\sqrt{3}} by multiplying numerator and denominator by 2+\sqrt{3}.

$$B=\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+\frac{1}{2+\sqrt{3}}+2014$$

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

$$B=\frac{2+\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+\frac{1}{2+\sqrt{3}}+2014$$

Square 2. Square \sqrt{3}.

$$B=\frac{2+\sqrt{3}}{4-3}+\frac{1}{2+\sqrt{3}}+2014$$

Subtract 3 from 4 to get 1.

$$B=\frac{2+\sqrt{3}}{1}+\frac{1}{2+\sqrt{3}}+2014$$

Anything divided by one gives itself.

$$B=2+\sqrt{3}+\frac{1}{2+\sqrt{3}}+2014$$

Rationalize the denominator of \frac{1}{2+\sqrt{3}} by multiplying numerator and denominator by 2-\sqrt{3}.

$$B=2+\sqrt{3}+\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+2014$$

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

$$B=2+\sqrt{3}+\frac{2-\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+2014$$

Square 2. Square \sqrt{3}.

$$B=2+\sqrt{3}+\frac{2-\sqrt{3}}{4-3}+2014$$

Subtract 3 from 4 to get 1.

$$B=2+\sqrt{3}+\frac{2-\sqrt{3}}{1}+2014$$

Anything divided by one gives itself.

$$B=2+\sqrt{3}+2-\sqrt{3}+2014$$

Add 2 and 2 to get 4.

$$B=4+\sqrt{3}-\sqrt{3}+2014$$

Combine \sqrt{3} and -\sqrt{3} to get 0.

$$B=4+2014$$

Add 4 and 2014 to get 2018.

$$B=2018$$

Assign B

$$B≔2018$$