Pre-Algebra Examples

$\frac{\frac{r^{2} - s^{2}}{r - s}}{\frac{r}{r^{2} + r s}}$

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 $b = s$ .

$\frac{\frac{(r + s) (r - s)}{r - s}}{\frac{r}{r^{2} + r s}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{(r + s) (r - s)}{r - s}$ by cancelling the common factors.

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Step 2.1.1

Cancel the common factor.

$\frac{\frac{(r + s) (r - s)}{r - s}}{\frac{r}{r^{2} + r s}}$

Step 2.1.2

Rewrite the expression.

$\frac{\frac{r + s}{1}}{\frac{r}{r^{2} + r s}}$

Step 2.2

Divide $r + s$ by $1$ .

$\frac{r + s}{\frac{r}{r^{2} + r s}}$

Step 3

Factor $r$ out of $r^{2} + r s$ .

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Step 3.1

Factor $r$ out of $r^{2}$ .

$\frac{r + s}{\frac{r}{r \cdot r + r s}}$

Step 3.2

Factor $r$ out of $r s$ .

$\frac{r + s}{\frac{r}{r \cdot r + r (s)}}$

Step 3.3

Factor $r$ out of $r \cdot r + r (s)$ .

$\frac{r + s}{\frac{r}{r (r + s)}}$

Step 4

Reduce the expression $\frac{r}{r (r + s)}$ by cancelling the common factors.

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Step 4.1

Cancel the common factor.

$\frac{r + s}{\frac{r}{r (r + s)}}$

Step 4.2

Rewrite the expression.

$\frac{r + s}{\frac{1}{r + s}}$