Basic Math Examples

$\frac{n}{a - 5} - \frac{2 n}{5 - a}$

Step 1

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{n}{a - 5} - \frac{2 n}{- 1 (- 5) - a}$

Step 2

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

$\frac{n}{a - 5} - \frac{2 n}{- 1 (- 5) - (a)}$

Step 3

Factor $- 1$ out of $- 1 (- 5) - (a)$ .

$\frac{n}{a - 5} - \frac{2 n}{- 1 (- 5 + a)}$

Step 4

Reorder terms.

$\frac{n}{a - 5} - \frac{2 n}{- 1 (a - 5)}$

Step 5

To write $\frac{n}{a - 5}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{n}{a - 5} \cdot \frac{- 1}{- 1} - \frac{2 n}{- 1 (a - 5)}$

Step 6

Write each expression with a common denominator of $(a - 5) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{n}{a - 5}$ by $\frac{- 1}{- 1}$ .

$\frac{n \cdot - 1}{(a - 5) \cdot - 1} - \frac{2 n}{- 1 (a - 5)}$

Step 6.2

Reorder the factors of $(a - 5) \cdot - 1$ .

$\frac{n \cdot - 1}{- (a - 5)} - \frac{2 n}{- 1 (a - 5)}$

Step 7

Combine the numerators over the common denominator.

$\frac{n \cdot - 1 - 2 n}{- (a - 5)}$

Step 8

Simplify the numerator.

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Step 8.1

Move $- 1$ to the left of $n$ .

$\frac{- 1 \cdot n - 2 n}{- (a - 5)}$

Step 8.2

Rewrite $- 1 n$ as $- n$ .

$\frac{- n - 2 n}{- (a - 5)}$

Step 8.3

Subtract $2 n$ from $- n$ .

$\frac{- 3 n}{- (a - 5)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{3 n}{a - 5}$