Solve 3+x/sqrt{3}=x-3

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

Solve for x

$$x=3\sqrt{3}+9\approx 14.196152423$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Subtract x from both sides.

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

Subtract 3 from both sides.

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

Subtract 3 from -3 to get -6.

$$\frac{x\sqrt{3}}{3}-x=-6$$

Multiply both sides of the equation by 3.

$$x\sqrt{3}-3x=-18$$

Combine all terms containing x.

$$\left(\sqrt{3}-3\right)x=-18$$

Divide both sides by \sqrt{3}-3.

$$\frac{\left(\sqrt{3}-3\right)x}{\sqrt{3}-3}=-\frac{18}{\sqrt{3}-3}$$

Dividing by \sqrt{3}-3 undoes the multiplication by \sqrt{3}-3.

$$x=-\frac{18}{\sqrt{3}-3}$$

Divide -18 by \sqrt{3}-3.

$$x=3\sqrt{3}+9$$