Basic Math Examples

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

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = r

$a = r$ and

b = s

$b = s$ .

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

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of

r + s

$r + s$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Divide

$r - s$ by

$1$ .

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

Step 3.2

Factor

$r$ out of

$r^{2} + s r$ .

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Step 3.2.1

Factor

$r$ out of

$r^{2}$ .

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

Step 3.2.2

Factor

$r$ out of

$s r$ .

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

Step 3.2.3

Factor

$r$ out of

$r \cdot r + r s$ .

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

Step 3.3

Cancel the common factor of

$r$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Divide

$r + s$ by

$1$ .

$(r - s) (r + s)$

Step 4

Expand

$(r - s) (r + s)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$r (r + s) - s (r + s)$

Step 4.2

Apply the distributive property.

$r \cdot r + r s - s (r + s)$

Step 4.3

Apply the distributive property.

$r \cdot r + r s - s r - s \cdot s$

Step 5

Simplify terms.

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Step 5.1

Combine the opposite terms in

$r \cdot r + r s - s r - s \cdot s$ .

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Step 5.1.1

Reorder the factors in the terms

$r s$ and

$- s r$ .

$r \cdot r + r s - r s - s \cdot s$

Step 5.1.2

Subtract

$r s$ from

$r s$ .

$r \cdot r + 0 - s \cdot s$

Step 5.1.3

Add

$r \cdot r$ and

$0$ .

$r \cdot r - s \cdot s$

Step 5.2

Simplify each term.

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Step 5.2.1

Multiply

$r$ by

$r$ .

$r^{2} - s \cdot s$

Step 5.2.2

Multiply

$s$ by

$s$ by adding the exponents.

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Step 5.2.2.1

Move

$s$ .

$r^{2} - (s \cdot s)$

Step 5.2.2.2

Multiply

$s$ by

$s$ .

$r^{2} - s^{2}$