Solve frac{sqrt{2}+1}{x}=0.5/sqrt{2-1}

$$\frac{ \sqrt{ 2 } +1 }{ x } = \frac{ 0.5 }{ \sqrt{ 2 } -1 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\sqrt{2}+1=\left(x\times 2^{\frac{1}{2}}+x\right)\times 0.5$$

Use the distributive property to multiply x\times 2^{\frac{1}{2}}+x by 0.5.

$$\sqrt{2}+1=x\times 2^{\frac{1}{2}}\times 0.5+0.5x$$

Swap sides so that all variable terms are on the left hand side.

$$x\times 2^{\frac{1}{2}}\times 0.5+0.5x=\sqrt{2}+1$$

Reorder the terms.

$$0.5\sqrt{2}x+0.5x=\sqrt{2}+1$$

Combine all terms containing x.

$$\left(0.5\sqrt{2}+0.5\right)x=\sqrt{2}+1$$

The equation is in standard form.

$$\frac{\sqrt{2}+1}{2}x=\sqrt{2}+1$$

Divide both sides by 0.5\sqrt{2}+0.5.

$$\frac{2\times \frac{\sqrt{2}+1}{2}x}{\sqrt{2}+1}=\frac{2\left(\sqrt{2}+1\right)}{\sqrt{2}+1}$$

Dividing by 0.5\sqrt{2}+0.5 undoes the multiplication by 0.5\sqrt{2}+0.5.

$$x=\frac{2\left(\sqrt{2}+1\right)}{\sqrt{2}+1}$$

Divide \sqrt{2}+1 by 0.5\sqrt{2}+0.5.

$$x=2$$