Solve B=1/3sqrt{3-1}

$$B = \frac { 1 } { 3 \sqrt { 3 } - 1 }$$

Solve for B

$$B=\frac{3\sqrt{3}+1}{26}\approx 0.238313555$$

Steps for Solving Linear Equation

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

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

Consider \left(3\sqrt{3}-1\right)\left(3\sqrt{3}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$B=\frac{3\sqrt{3}+1}{9\left(\sqrt{3}\right)^{2}-1^{2}}$$

The square of \sqrt{3} is 3.

$$B=\frac{3\sqrt{3}+1}{9\times 3-1^{2}}$$

Multiply 9 and 3 to get 27.

$$B=\frac{3\sqrt{3}+1}{27-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$B=\frac{3\sqrt{3}+1}{27-1}$$

Subtract 1 from 27 to get 26.

$$B=\frac{3\sqrt{3}+1}{26}$$

Divide each term of 3\sqrt{3}+1 by 26 to get \frac{3}{26}\sqrt{3}+\frac{1}{26}.

$$B=\frac{3}{26}\sqrt{3}+\frac{1}{26}$$

Assign B

$$B≔\frac{3\sqrt{3}+1}{26}$$