Algebra Examples

$\frac{5}{x + y} + \frac{5}{x^{2} - y^{2}}$

Step 1

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 $b = y$ .

$\frac{5}{x + y} + \frac{5}{(x + y) (x - y)}$

Step 2

To write $\frac{5}{x + y}$ as a fraction with a common denominator, multiply by $\frac{x - y}{x - y}$ .

$\frac{5}{x + y} \cdot \frac{x - y}{x - y} + \frac{5}{(x + y) (x - y)}$

Step 3

Multiply $\frac{5}{x + y}$ by $\frac{x - y}{x - y}$ .

$\frac{5 (x - y)}{(x + y) (x - y)} + \frac{5}{(x + y) (x - y)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (x - y) + 5}{(x + y) (x - y)}$

Step 5

Factor $5$ out of $5 (x - y) + 5$ .

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Step 5.1

Factor $5$ out of $5$ .

$\frac{5 (x - y) + 5 (1)}{(x + y) (x - y)}$

Step 5.2

Factor $5$ out of $5 (x - y) + 5 (1)$ .

$\frac{5 (x - y + 1)}{(x + y) (x - y)}$