Solve x/8-x=sqrt{3}

$$\frac{ x }{ 8-x } = \sqrt{ 3 }$$

Solve for x

$$x=12-4\sqrt{3}\approx 5.07179677$$

Steps for Solving Linear Equation

Variable x cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by -x+8.

$$x=\left(-x+8\right)\sqrt{3}$$

Use the distributive property to multiply -x+8 by \sqrt{3}.

$$x=-x\sqrt{3}+8\sqrt{3}$$

Add x\sqrt{3} to both sides.

$$x+x\sqrt{3}=8\sqrt{3}$$

Combine all terms containing x.

$$\left(1+\sqrt{3}\right)x=8\sqrt{3}$$

The equation is in standard form.

$$\left(\sqrt{3}+1\right)x=8\sqrt{3}$$

Divide both sides by 1+\sqrt{3}.

$$\frac{\left(\sqrt{3}+1\right)x}{\sqrt{3}+1}=\frac{8\sqrt{3}}{\sqrt{3}+1}$$

Dividing by 1+\sqrt{3} undoes the multiplication by 1+\sqrt{3}.

$$x=\frac{8\sqrt{3}}{\sqrt{3}+1}$$

Divide 8\sqrt{3} by 1+\sqrt{3}.

$$x=12-4\sqrt{3}$$