Pre-Algebra Examples

$\frac{r}{r^{2} - q^{2}} + \frac{5}{r + q}$

Step 1

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

$\frac{r}{(r + q) (r - q)} + \frac{5}{r + q}$

Step 2

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

$\frac{r}{(r + q) (r - q)} + \frac{5}{r + q} \cdot \frac{r - q}{r - q}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{5}{r + q}$ by $\frac{r - q}{r - q}$ .

$\frac{r}{(r + q) (r - q)} + \frac{5 (r - q)}{(r + q) (r - q)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{r + 5 (r - q)}{(r + q) (r - q)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{r + 5 r + 5 (- q)}{(r + q) (r - q)}$

Step 4.2

Multiply $- 1$ by $5$ .

$\frac{r + 5 r - 5 q}{(r + q) (r - q)}$

Step 4.3

Add $r$ and $5 r$ .

$\frac{6 r - 5 q}{(r + q) (r - q)}$