Solve 1/sqrt{1^2+1}-frac{sqrt{1^2+1}}{1^2}

$$\frac{ 1 }{ \sqrt{ { 1 }^{ 2 } +1 } } - \frac{ \sqrt{ { 1 }^{ 2 } +1 } }{ { 1 }^{ 2 } }$$

Evaluate

$$-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\sqrt{1+1}}-\frac{\sqrt{1^{2}+1}}{1^{2}}$$

Add 1 and 1 to get 2.

$$\frac{1}{\sqrt{2}}-\frac{\sqrt{1^{2}+1}}{1^{2}}$$

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

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{1^{2}+1}}{1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{1+1}}{1^{2}}$$

Add 1 and 1 to get 2.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{1}$$

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{2}-\sqrt{2}$$

Combine \frac{\sqrt{2}}{2} and -\sqrt{2} to get -\frac{1}{2}\sqrt{2}.

$$-\frac{1}{2}\sqrt{2}$$