Solve 1-2*1/k^2/1+frac{1{k^2}}

$$\frac { 1 - 2 \cdot \frac { 1 } { k ^ { 2 } } } { 1 + \frac { 1 } { k ^ { 2 } } }$$

Evaluate

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

Solution Steps

Express 2\times \frac{1}{k^{2}} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{k^{2}}{k^{2}}.

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

Since \frac{k^{2}}{k^{2}} and \frac{2}{k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{k^{2}}{k^{2}}.

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

Since \frac{k^{2}}{k^{2}} and \frac{1}{k^{2}} have the same denominator, add them by adding their numerators.

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

Divide \frac{k^{2}-2}{k^{2}} by \frac{k^{2}+1}{k^{2}} by multiplying \frac{k^{2}-2}{k^{2}} by the reciprocal of \frac{k^{2}+1}{k^{2}}.

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

Cancel out k^{2} in both numerator and denominator.

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

Expand

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

Solution Steps

Express 2\times \frac{1}{k^{2}} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{k^{2}}{k^{2}}.

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

Since \frac{k^{2}}{k^{2}} and \frac{2}{k^{2}} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{k^{2}}{k^{2}}.

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

Since \frac{k^{2}}{k^{2}} and \frac{1}{k^{2}} have the same denominator, add them by adding their numerators.

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

Divide \frac{k^{2}-2}{k^{2}} by \frac{k^{2}+1}{k^{2}} by multiplying \frac{k^{2}-2}{k^{2}} by the reciprocal of \frac{k^{2}+1}{k^{2}}.

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

Cancel out k^{2} in both numerator and denominator.

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