Basic Math Examples

$\frac{m^{2} + 5 m + 6}{m + 3} \cdot \frac{m^{2} + m - 6}{m^{2} + 3 m + 2}$

Step 1

Factor $m^{2} + 5 m + 6$ using the AC method.

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Step 1.1

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 $6$ and whose sum is $5$ .

$2, 3$

Step 1.2

Write the factored form using these integers.

$\frac{(m + 2) (m + 3)}{m + 3} \cdot \frac{m^{2} + m - 6}{m^{2} + 3 m + 2}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{(m + 2) (m + 3)}{m + 3}$ by cancelling the common factors.

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Step 2.1.1

Cancel the common factor.

$\frac{(m + 2) (m + 3)}{m + 3} \cdot \frac{m^{2} + m - 6}{m^{2} + 3 m + 2}$

Step 2.1.2

Rewrite the expression.

$\frac{m + 2}{1} \cdot \frac{m^{2} + m - 6}{m^{2} + 3 m + 2}$

Step 2.2

Divide $m + 2$ by $1$ .

$(m + 2) \cdot \frac{m^{2} + m - 6}{m^{2} + 3 m + 2}$

Step 3

Factor $m^{2} + m - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 3.2

Write the factored form using these integers.

$(m + 2) \cdot \frac{(m - 2) (m + 3)}{m^{2} + 3 m + 2}$

Step 4

Factor $m^{2} + 3 m + 2$ using the AC method.

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Step 4.1

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 $3$ .

$1, 2$

Step 4.2

Write the factored form using these integers.

$(m + 2) \cdot \frac{(m - 2) (m + 3)}{(m + 1) (m + 2)}$