Algebra Examples

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

Step 1

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

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Step 1.1

Factor $3$ out of $3 x$ .

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

Step 1.2

Factor $3$ out of $3 y$ .

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

Step 1.3

Factor $3$ out of $3 (x) + 3 (y)$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x - y$ .

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Step 3.1.1

Factor $x - y$ out of ${(x - y)}^{2}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x + y$ .

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Step 3.2.1

Factor $x + y$ out of $3 (x + y)$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.3

Multiply $x - y$ by $\frac{3}{x + y}$ .

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

Step 3.4

Move $3$ to the left of $x - y$ .

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