Solve 1/c+1/d-c-d/cd

$$\frac { 1 } { c } + \frac { 1 } { d } - \frac { c - d } { c d }$$

Evaluate

$$\frac{2}{c}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c and d is cd. Multiply \frac{1}{c} times \frac{d}{d}. Multiply \frac{1}{d} times \frac{c}{c}.

$$\frac{d}{cd}+\frac{c}{cd}-\frac{c-d}{cd}$$

Since \frac{d}{cd} and \frac{c}{cd} have the same denominator, add them by adding their numerators.

$$\frac{d+c}{cd}-\frac{c-d}{cd}$$

Since \frac{d+c}{cd} and \frac{c-d}{cd} have the same denominator, subtract them by subtracting their numerators.

$$\frac{d+c-\left(c-d\right)}{cd}$$

Do the multiplications in d+c-\left(c-d\right).

$$\frac{d+c-c+d}{cd}$$

Combine like terms in d+c-c+d.

$$\frac{2d}{cd}$$

Cancel out d in both numerator and denominator.

$$\frac{2}{c}$$

Expand

$$\frac{2}{c}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c and d is cd. Multiply \frac{1}{c} times \frac{d}{d}. Multiply \frac{1}{d} times \frac{c}{c}.

$$\frac{d}{cd}+\frac{c}{cd}-\frac{c-d}{cd}$$

Since \frac{d}{cd} and \frac{c}{cd} have the same denominator, add them by adding their numerators.

$$\frac{d+c}{cd}-\frac{c-d}{cd}$$

Since \frac{d+c}{cd} and \frac{c-d}{cd} have the same denominator, subtract them by subtracting their numerators.

$$\frac{d+c-\left(c-d\right)}{cd}$$

Do the multiplications in d+c-\left(c-d\right).

$$\frac{d+c-c+d}{cd}$$

Combine like terms in d+c-c+d.

$$\frac{2d}{cd}$$

Cancel out d in both numerator and denominator.

$$\frac{2}{c}$$