Solve d^2/d-c+c^2/c-d

$$\frac { d ^ { 2 } } { d - c } + \frac { c ^ { 2 } } { c - d }$$

Evaluate

$$c+d$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of d-c and c-d is c-d. Multiply \frac{d^{2}}{d-c} times \frac{-1}{-1}.

$$\frac{-d^{2}}{c-d}+\frac{c^{2}}{c-d}$$

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

$$\frac{-d^{2}+c^{2}}{c-d}$$

Factor the expressions that are not already factored in \frac{-d^{2}+c^{2}}{c-d}.

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

Extract the negative sign in d-c.

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

Cancel out c-d in both numerator and denominator.

$$-\left(-c-d\right)$$

Expand the expression.

$$c+d$$

Differentiate w.r.t. d

$$1$$