Basic Math Examples

$\frac{- 7 m^{4} + 15 m^{3} - 12 m^{2} + (3 m^{5} - 12 m - 7 m^{3})}{m - 6}$

Step 1

Remove parentheses.

$\frac{- 7 m^{4} + 15 m^{3} - 12 m^{2} + 3 m^{5} - 12 m - 7 m^{3}}{m - 6}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $7 m^{3}$ from $15 m^{3}$ .

$\frac{- 7 m^{4} + 8 m^{3} - 12 m^{2} + 3 m^{5} - 12 m}{m - 6}$

Step 2.2

Factor $m$ out of $- 7 m^{4} + 8 m^{3} - 12 m^{2} + 3 m^{5} - 12 m$ .

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Step 2.2.1

Factor $m$ out of $- 7 m^{4}$ .

$\frac{m (- 7 m^{3}) + 8 m^{3} - 12 m^{2} + 3 m^{5} - 12 m}{m - 6}$

Step 2.2.2

Factor $m$ out of $8 m^{3}$ .

$\frac{m (- 7 m^{3}) + m (8 m^{2}) - 12 m^{2} + 3 m^{5} - 12 m}{m - 6}$

Step 2.2.3

Factor $m$ out of $- 12 m^{2}$ .

$\frac{m (- 7 m^{3}) + m (8 m^{2}) + m (- 12 m) + 3 m^{5} - 12 m}{m - 6}$

Step 2.2.4

Factor $m$ out of $3 m^{5}$ .

$\frac{m (- 7 m^{3}) + m (8 m^{2}) + m (- 12 m) + m (3 m^{4}) - 12 m}{m - 6}$

Step 2.2.5

Factor $m$ out of $- 12 m$ .

$\frac{m (- 7 m^{3}) + m (8 m^{2}) + m (- 12 m) + m (3 m^{4}) + m \cdot - 12}{m - 6}$

Step 2.2.6

Factor $m$ out of $m (- 7 m^{3}) + m (8 m^{2})$ .

$\frac{m (- 7 m^{3} + 8 m^{2}) + m (- 12 m) + m (3 m^{4}) + m \cdot - 12}{m - 6}$

Step 2.2.7

Factor $m$ out of $m (- 7 m^{3} + 8 m^{2}) + m (- 12 m)$ .

$\frac{m (- 7 m^{3} + 8 m^{2} - 12 m) + m (3 m^{4}) + m \cdot - 12}{m - 6}$

Step 2.2.8

Factor $m$ out of $m (- 7 m^{3} + 8 m^{2} - 12 m) + m (3 m^{4})$ .

$\frac{m (- 7 m^{3} + 8 m^{2} - 12 m + 3 m^{4}) + m \cdot - 12}{m - 6}$

Step 2.2.9

Factor $m$ out of $m (- 7 m^{3} + 8 m^{2} - 12 m + 3 m^{4}) + m \cdot - 12$ .

$\frac{m (- 7 m^{3} + 8 m^{2} - 12 m + 3 m^{4} - 12)}{m - 6}$

Step 2.3

Reorder terms.

$\frac{m (3 m^{4} - 7 m^{3} + 8 m^{2} - 12 m - 12)}{m - 6}$