Solve t+1/t/t-frac{2{t}}

$$\frac { t + \frac { 1 } { t } } { t - \frac { 2 } { t } }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{tt}{t}+\frac{1}{t}}{t-\frac{2}{t}}$$

Since \frac{tt}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

$$\frac{\frac{tt+1}{t}}{t-\frac{2}{t}}$$

Do the multiplications in tt+1.

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

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

$$\frac{\frac{t^{2}+1}{t}}{\frac{tt}{t}-\frac{2}{t}}$$

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

$$\frac{\frac{t^{2}+1}{t}}{\frac{tt-2}{t}}$$

Do the multiplications in tt-2.

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

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

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

Cancel out t in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{tt}{t}+\frac{1}{t}}{t-\frac{2}{t}}$$

Since \frac{tt}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

$$\frac{\frac{tt+1}{t}}{t-\frac{2}{t}}$$

Do the multiplications in tt+1.

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

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

$$\frac{\frac{t^{2}+1}{t}}{\frac{tt}{t}-\frac{2}{t}}$$

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

$$\frac{\frac{t^{2}+1}{t}}{\frac{tt-2}{t}}$$

Do the multiplications in tt-2.

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

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

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

Cancel out t in both numerator and denominator.

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