Linear Algebra Examples

$\frac{5}{x - y} + \frac{9}{y - x} + \frac{4}{x - y}$

Step 1

Combine the numerators over the common denominator.

$\frac{5 + 4}{x - y} + \frac{9}{- x + y}$

Step 2

Add $5$ and $4$ .

$\frac{9}{x - y} + \frac{9}{- x + y}$

Step 3

Factor $- 1$ out of $- x$ .

$\frac{9}{x - y} + \frac{9}{- (x) + y}$

Step 4

Factor $- 1$ out of $y$ .

$\frac{9}{x - y} + \frac{9}{- (x) - 1 (- y)}$

Step 5

Factor $- 1$ out of $- (x) - 1 (- y)$ .

$\frac{9}{x - y} + \frac{9}{- (x - y)}$

Step 6

Move a negative from the denominator of $\frac{9}{- (x - y)}$ to the numerator.

$\frac{9}{x - y} + \frac{- 1 \cdot 9}{x - y}$

Step 7

Combine the numerators over the common denominator.

$\frac{9 - 1 \cdot 9}{x - y}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 1$ by $9$ .

$\frac{9 - 9}{x - y}$

Step 8.2

Subtract $9$ from $9$ .

$\frac{0}{x - y}$

Step 9

Divide $0$ by $x - y$ .

$0$