Solve x/100+x/sqrt{3}=1/sqrt{3}

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

Solve for x

$$x=\frac{10000-100\sqrt{3}}{9997}\approx 0.982974384$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100.

$$x+\frac{100}{3}\times 3^{\frac{1}{2}}x=\frac{100}{3}\times 3^{\frac{1}{2}}$$

Reorder the terms.

$$\frac{100}{3}\sqrt{3}x+x=\frac{100}{3}\sqrt{3}$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by \frac{100}{3}\sqrt{3}+1.

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

Dividing by \frac{100}{3}\sqrt{3}+1 undoes the multiplication by \frac{100}{3}\sqrt{3}+1.

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

Divide \frac{100\sqrt{3}}{3} by \frac{100}{3}\sqrt{3}+1.

$$x=\frac{10000-100\sqrt{3}}{9997}$$