Solve frac{sqrt{3}}{2}=frac{2sqrt{3}+9}{3+x}

$$\frac{ \sqrt{ 3 } }{ 2 } = \frac{ 2 \sqrt{ 3 } +9 }{ 3+x }$$

Solve for x

$$x=6\sqrt{3}+1\approx 11.392304845$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+3\right), the least common multiple of 2,3+x.

$$\left(x+3\right)\sqrt{3}=2\left(2\sqrt{3}+9\right)$$

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

$$x\sqrt{3}+3\sqrt{3}=2\left(2\sqrt{3}+9\right)$$

Use the distributive property to multiply 2 by 2\sqrt{3}+9.

$$x\sqrt{3}+3\sqrt{3}=4\sqrt{3}+18$$

Subtract 3\sqrt{3} from both sides.

$$x\sqrt{3}=4\sqrt{3}+18-3\sqrt{3}$$

Combine 4\sqrt{3} and -3\sqrt{3} to get \sqrt{3}.

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

The equation is in standard form.

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

Divide both sides by \sqrt{3}.

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

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

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

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

$$x=6\sqrt{3}+1$$