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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

The square of \sqrt{2} is 2.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

Multiply both sides of the equation by 2.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}.

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

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

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

Divide 2\sqrt{2} by \sqrt{2}.

$$x=2$$