Pre-Algebra Examples

$\frac{2 a}{a - n} + \frac{2 n}{n - a}$

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $n$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Simplify the expression.

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Step 1.4.1

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

$\frac{2 a}{a - n} + \frac{- (2 n)}{- n + a}$

Step 1.4.2

Reorder terms.

$\frac{2 a}{a - n} + \frac{- (2 n)}{a - n}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 a - (2 n)}{a - n}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $2$ .

$\frac{2 a - 2 n}{a - n}$

Step 2.2

Factor $2$ out of $2 a - 2 n$ .

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Step 2.2.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) - 2 n}{a - n}$

Step 2.2.2

Factor $2$ out of $- 2 n$ .

$\frac{2 (a) + 2 (- n)}{a - n}$

Step 2.2.3

Factor $2$ out of $2 (a) + 2 (- n)$ .

$\frac{2 (a - n)}{a - n}$

Step 3

Cancel the common factor of $a - n$ .

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Step 3.1

Cancel the common factor.

$\frac{2 (a - n)}{a - n}$

Step 3.2

Divide $2$ by $1$ .

$2$