Finite Math Examples

$\frac{7 m^{2} + 42 m - 49}{m + 7}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $7$ out of $7 m^{2} + 42 m - 49$ .

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Step 1.1.1

Factor $7$ out of $7 m^{2}$ .

$\frac{7 (m^{2}) + 42 m - 49}{m + 7}$

Step 1.1.2

Factor $7$ out of $42 m$ .

$\frac{7 (m^{2}) + 7 (6 m) - 49}{m + 7}$

Step 1.1.3

Factor $7$ out of $- 49$ .

$\frac{7 m^{2} + 7 (6 m) + 7 \cdot - 7}{m + 7}$

Step 1.1.4

Factor $7$ out of $7 m^{2} + 7 (6 m)$ .

$\frac{7 (m^{2} + 6 m) + 7 \cdot - 7}{m + 7}$

Step 1.1.5

Factor $7$ out of $7 (m^{2} + 6 m) + 7 \cdot - 7$ .

$\frac{7 (m^{2} + 6 m - 7)}{m + 7}$

Step 1.2

Factor $m^{2} + 6 m - 7$ using the AC method.

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Step 1.2.1

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 $- 7$ and whose sum is $6$ .

$- 1, 7$

Step 1.2.2

Write the factored form using these integers.

$\frac{7 ((m - 1) (m + 7))}{m + 7}$

$\frac{7 (m - 1) (m + 7)}{m + 7}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $m + 7$ .

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Step 2.1.1

Cancel the common factor.

$\frac{7 (m - 1) (m + 7)}{m + 7}$

Step 2.1.2

Divide $7 (m - 1)$ by $1$ .

$7 (m - 1)$

Step 2.2

Apply the distributive property.

$7 m + 7 \cdot - 1$

Step 2.3

Multiply $7$ by $- 1$ .

$7 m - 7$