Solve 1/frac{1{2}}=x/sqrt{2/2}

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

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

Steps for Solving Linear Equation

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

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

Multiply 1 and 2 to get 2.

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

Divide x by \frac{\sqrt{2}}{2} by multiplying x by the reciprocal of \frac{\sqrt{2}}{2}.

$$2=\frac{x\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{x\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$2=\frac{x\times 2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$2=x\sqrt{2}$$

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

$$x\sqrt{2}=2$$

The equation is in standard form.

$$\sqrt{2}x=2$$

Divide both sides by \sqrt{2}.

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

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

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

Divide 2 by \sqrt{2}.

$$x=\sqrt{2}$$