Solve x=frac{10sqrt{3}}{3-sqrt{3}}*3+sqrt{3}

$$x = \frac { 10 \sqrt { 3 } } { 3 - \sqrt { 3 } } \cdot 3 + \sqrt { 3 }$$

Solve for x

$$x=16\sqrt{3}+15\approx 42.712812921$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{10\sqrt{3}}{3-\sqrt{3}} by multiplying numerator and denominator by 3+\sqrt{3}.

$$x=3\times \frac{10\sqrt{3}\left(3+\sqrt{3}\right)}{\left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right)}+\sqrt{3}$$

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

$$x=3\times \frac{10\sqrt{3}\left(3+\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}+\sqrt{3}$$

Square 3. Square \sqrt{3}.

$$x=3\times \frac{10\sqrt{3}\left(3+\sqrt{3}\right)}{9-3}+\sqrt{3}$$

Subtract 3 from 9 to get 6.

$$x=3\times \frac{10\sqrt{3}\left(3+\sqrt{3}\right)}{6}+\sqrt{3}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$x=\frac{10\sqrt{3}\left(3+\sqrt{3}\right)}{2}+\sqrt{3}$$

Use the distributive property to multiply 10\sqrt{3} by 3+\sqrt{3}.

$$x=\frac{30\sqrt{3}+10\left(\sqrt{3}\right)^{2}}{2}+\sqrt{3}$$

The square of \sqrt{3} is 3.

$$x=\frac{30\sqrt{3}+10\times 3}{2}+\sqrt{3}$$

Multiply 10 and 3 to get 30.

$$x=\frac{30\sqrt{3}+30}{2}+\sqrt{3}$$

Divide each term of 30\sqrt{3}+30 by 2 to get 15\sqrt{3}+15.

$$x=15\sqrt{3}+15+\sqrt{3}$$

Combine 15\sqrt{3} and \sqrt{3} to get 16\sqrt{3}.

$$x=16\sqrt{3}+15$$

Assign x

$$x≔16\sqrt{3}+15$$