Solve frac{100sqrt{3}}{1-sqrt{3}}=x

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

Solve for x

$$x=-50\sqrt{3}-150\approx -236.602540378$$

Steps for Solving Linear Equation

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

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

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

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

Square 1. Square \sqrt{3}.

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

Subtract 3 from 1 to get -2.

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

Use the distributive property to multiply 100\sqrt{3} by 1+\sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{100\sqrt{3}+100\times 3}{-2}=x$$

Multiply 100 and 3 to get 300.

$$\frac{100\sqrt{3}+300}{-2}=x$$

Divide each term of 100\sqrt{3}+300 by -2 to get -50\sqrt{3}-150.

$$-50\sqrt{3}-150=x$$

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

$$x=-50\sqrt{3}-150$$