Solve u-1/u/u+frac{1{u}}

$$\frac { u - \frac { 1 } { u } } { u + \frac { 1 } { u } }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{uu}{u}-\frac{1}{u}}{u+\frac{1}{u}}$$

Since \frac{uu}{u} and \frac{1}{u} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{uu-1}{u}}{u+\frac{1}{u}}$$

Do the multiplications in uu-1.

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

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

$$\frac{\frac{u^{2}-1}{u}}{\frac{uu}{u}+\frac{1}{u}}$$

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

$$\frac{\frac{u^{2}-1}{u}}{\frac{uu+1}{u}}$$

Do the multiplications in uu+1.

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

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

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

Cancel out u in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{uu}{u}-\frac{1}{u}}{u+\frac{1}{u}}$$

Since \frac{uu}{u} and \frac{1}{u} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{uu-1}{u}}{u+\frac{1}{u}}$$

Do the multiplications in uu-1.

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

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

$$\frac{\frac{u^{2}-1}{u}}{\frac{uu}{u}+\frac{1}{u}}$$

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

$$\frac{\frac{u^{2}-1}{u}}{\frac{uu+1}{u}}$$

Do the multiplications in uu+1.

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

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

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

Cancel out u in both numerator and denominator.

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