Solve 1/2(u+1/u)-u

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in uu+1.

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

Multiply \frac{1}{2} times \frac{u^{2}+1}{u} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Since \frac{u^{2}+1}{2u} and \frac{u\times 2u}{2u} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in u^{2}+1-u\times 2u.

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

Combine like terms in u^{2}+1-2u^{2}.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in uu+1.

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

Multiply \frac{1}{2} times \frac{u^{2}+1}{u} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Since \frac{u^{2}+1}{2u} and \frac{u\times 2u}{2u} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in u^{2}+1-u\times 2u.

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

Combine like terms in u^{2}+1-2u^{2}.

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