Basic Math Examples

$\frac{y^{2} + 6 y + 8}{y^{2} + y - 2} \div \frac{y + 4}{2 y + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} + 6 y + 8}{y^{2} + y - 2} \cdot \frac{2 y + 4}{y + 4}$

Step 2

Factor $y^{2} + 6 y + 8$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $6$ .

$2, 4$

Step 2.2

Write the factored form using these integers.

$\frac{(y + 2) (y + 4)}{y^{2} + y - 2} \cdot \frac{2 y + 4}{y + 4}$

Step 3

Factor $y^{2} + y - 2$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Step 3.2

Write the factored form using these integers.

$\frac{(y + 2) (y + 4)}{(y - 1) (y + 2)} \cdot \frac{2 y + 4}{y + 4}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $y + 4$ .

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Step 4.1.1

Factor $y + 4$ out of $(y + 2) (y + 4)$ .

$\frac{(y + 4) (y + 2)}{(y - 1) (y + 2)} \cdot \frac{2 y + 4}{y + 4}$

Step 4.1.2

Cancel the common factor.

$\frac{(y + 4) (y + 2)}{(y - 1) (y + 2)} \cdot \frac{2 y + 4}{y + 4}$

Step 4.1.3

Rewrite the expression.

$\frac{y + 2}{(y - 1) (y + 2)} (2 y + 4)$

Step 4.2

Cancel the common factor of $y + 2$ .

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Step 4.2.1

Cancel the common factor.

$\frac{y + 2}{(y - 1) (y + 2)} (2 y + 4)$

Step 4.2.2

Rewrite the expression.

$\frac{1}{y - 1} (2 y + 4)$

Step 4.3

Multiply $\frac{1}{y - 1}$ by $2 y + 4$ .

$\frac{2 y + 4}{y - 1}$

Step 4.4

Factor $2$ out of $2 y + 4$ .

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Step 4.4.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) + 4}{y - 1}$

Step 4.4.2

Factor $2$ out of $4$ .

$\frac{2 y + 2 \cdot 2}{y - 1}$

Step 4.4.3

Factor $2$ out of $2 y + 2 \cdot 2$ .

$\frac{2 (y + 2)}{y - 1}$