Finite Math Examples

$\frac{48 x^{11} - 12 x^{10} + 30 x^{8} + 12 x^{6} + 5 x^{5}}{6 x^{8}}$

Step 1

Factor $x^{5}$ out of $48 x^{11} - 12 x^{10} + 30 x^{8} + 12 x^{6} + 5 x^{5}$ .

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Step 1.1

Factor $x^{5}$ out of $48 x^{11}$ .

$\frac{x^{5} (48 x^{6}) - 12 x^{10} + 30 x^{8} + 12 x^{6} + 5 x^{5}}{6 x^{8}}$

Step 1.2

Factor $x^{5}$ out of $- 12 x^{10}$ .

$\frac{x^{5} (48 x^{6}) + x^{5} (- 12 x^{5}) + 30 x^{8} + 12 x^{6} + 5 x^{5}}{6 x^{8}}$

Step 1.3

Factor $x^{5}$ out of $30 x^{8}$ .

$\frac{x^{5} (48 x^{6}) + x^{5} (- 12 x^{5}) + x^{5} (30 x^{3}) + 12 x^{6} + 5 x^{5}}{6 x^{8}}$

Step 1.4

Factor $x^{5}$ out of $12 x^{6}$ .

$\frac{x^{5} (48 x^{6}) + x^{5} (- 12 x^{5}) + x^{5} (30 x^{3}) + x^{5} (12 x) + 5 x^{5}}{6 x^{8}}$

Step 1.5

Factor $x^{5}$ out of $5 x^{5}$ .

$\frac{x^{5} (48 x^{6}) + x^{5} (- 12 x^{5}) + x^{5} (30 x^{3}) + x^{5} (12 x) + x^{5} \cdot 5}{6 x^{8}}$

Step 1.6

Factor $x^{5}$ out of $x^{5} (48 x^{6}) + x^{5} (- 12 x^{5})$ .

$\frac{x^{5} (48 x^{6} - 12 x^{5}) + x^{5} (30 x^{3}) + x^{5} (12 x) + x^{5} \cdot 5}{6 x^{8}}$

Step 1.7

Factor $x^{5}$ out of $x^{5} (48 x^{6} - 12 x^{5}) + x^{5} (30 x^{3})$ .

$\frac{x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3}) + x^{5} (12 x) + x^{5} \cdot 5}{6 x^{8}}$

Step 1.8

Factor $x^{5}$ out of $x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3}) + x^{5} (12 x)$ .

$\frac{x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x) + x^{5} \cdot 5}{6 x^{8}}$

Step 1.9

Factor $x^{5}$ out of $x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x) + x^{5} \cdot 5$ .

$\frac{x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x + 5)}{6 x^{8}}$

Step 2

Cancel the common factors.

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Step 2.1

Factor $x^{5}$ out of $6 x^{8}$ .

$\frac{x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x + 5)}{x^{5} (6 x^{3})}$

Step 2.2

Cancel the common factor.

$\frac{x^{5} (48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x + 5)}{x^{5} (6 x^{3})}$

Step 2.3

Rewrite the expression.

$\frac{48 x^{6} - 12 x^{5} + 30 x^{3} + 12 x + 5}{6 x^{3}}$