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

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

Verify

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Combine \sqrt{2} and \frac{\sqrt{2}}{2} to get \frac{3}{2}\sqrt{2}.

$$\frac{3}{2}\sqrt{2}=\frac{\sqrt{2}}{1}+\frac{1}{\sqrt{2}}$$

Anything divided by one gives itself.

$$\frac{3}{2}\sqrt{2}=\sqrt{2}+\frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3}{2}\sqrt{2}=\sqrt{2}+\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3}{2}\sqrt{2}=\sqrt{2}+\frac{\sqrt{2}}{2}$$

Combine \sqrt{2} and \frac{\sqrt{2}}{2} to get \frac{3}{2}\sqrt{2}.

$$\frac{3}{2}\sqrt{2}=\frac{3}{2}\sqrt{2}$$

Subtract \frac{3}{2}\sqrt{2} from both sides.

$$\frac{3}{2}\sqrt{2}-\frac{3}{2}\sqrt{2}=0$$

Combine \frac{3}{2}\sqrt{2} and -\frac{3}{2}\sqrt{2} to get 0.

$$0=0$$

Compare 0 and 0.

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