Solve 100/sqrt{3-1}=x

$$\frac{ 100 }{ \sqrt{ 3 } -1 } =x$$

Solve for x

$$x=50\left(\sqrt{3}+1\right)\approx 136.602540378$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{100}{\sqrt{3}-1} by multiplying numerator and denominator by \sqrt{3}+1.

$$\frac{100\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=x$$

Consider \left(\sqrt{3}-1\right)\left(\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}.

$$\frac{100\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}=x$$

Square \sqrt{3}. Square 1.

$$\frac{100\left(\sqrt{3}+1\right)}{3-1}=x$$

Subtract 1 from 3 to get 2.

$$\frac{100\left(\sqrt{3}+1\right)}{2}=x$$

Divide 100\left(\sqrt{3}+1\right) by 2 to get 50\left(\sqrt{3}+1\right).

$$50\left(\sqrt{3}+1\right)=x$$

Use the distributive property to multiply 50 by \sqrt{3}+1.

$$50\sqrt{3}+50=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=50\sqrt{3}+50$$