Solve d^2/d-a+a^2/a-d

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

Evaluate

$$a+d$$

Short Solution Steps

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

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

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

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

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

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

Extract the negative sign in d-a.

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

Cancel out a-d in both numerator and denominator.

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

Expand the expression.

$$a+d$$

Differentiate w.r.t. d

$$1$$