Algebra Examples

$\frac{3 x + 6}{x + y} + \frac{6}{- x - y}$

Step 1

Simplify terms.

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Step 1.1

Factor $3$ out of $3 x + 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6}{x + y} + \frac{6}{- x - y}$

Step 1.1.2

Factor $3$ out of $6$ .

$\frac{3 x + 3 \cdot 2}{x + y} + \frac{6}{- x - y}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 (x + 2)}{x + y} + \frac{6}{- x - y}$

Step 1.2

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

$\frac{3 (x + 2)}{x + y} + \frac{6}{- (x) - y}$

Step 1.3

Factor $- 1$ out of $- y$ .

$\frac{3 (x + 2)}{x + y} + \frac{6}{- (x) - (y)}$

Step 1.4

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

$\frac{3 (x + 2)}{x + y} + \frac{6}{- (x + y)}$

Step 1.5

Move a negative from the denominator of $\frac{6}{- (x + y)}$ to the numerator.

$\frac{3 (x + 2)}{x + y} + \frac{- 1 \cdot 6}{x + y}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{3 (x + 2) - 1 \cdot 6}{x + y}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{3 x + 3 \cdot 2 - 1 \cdot 6}{x + y}$

Step 2.2

Multiply $3$ by $2$ .

$\frac{3 x + 6 - 1 \cdot 6}{x + y}$

Step 2.3

Multiply $- 1$ by $6$ .

$\frac{3 x + 6 - 6}{x + y}$

Step 2.4

Subtract $6$ from $6$ .

$\frac{3 x + 0}{x + y}$

Step 2.5

Add $3 x$ and $0$ .

$\frac{3 x}{x + y}$