Basic Math Examples

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

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $d$ .

$\frac{a^{2}}{a - d} + \frac{d^{2}}{- 1 (- d) - a}$

Step 1.2

Factor $- 1$ out of $- a$ .

$\frac{a^{2}}{a - d} + \frac{d^{2}}{- 1 (- d) - (a)}$

Step 1.3

Factor $- 1$ out of $- 1 (- d) - (a)$ .

$\frac{a^{2}}{a - d} + \frac{d^{2}}{- 1 (- d + a)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{d^{2}}{- 1 (- d + a)}$ to the numerator.

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

Step 1.4.2

Reorder terms.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = d$ .

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

Step 3

Cancel the common factor of $a - d$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $a + d$ by $1$ .

$a + d$