Finite Math Examples

$6 a^{4} b \div 54 a^{10} b^{11} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{6 a^{4} b}{54 a^{10} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.2

Cancel the common factor of $6$ and $54$ .

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Step 1.2.1

Factor $6$ out of $6 a^{4} b$ .

$\frac{6 (a^{4} b)}{54 a^{10} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $6$ out of $54 a^{10} b^{11}$ .

$\frac{6 (a^{4} b)}{6 (9 a^{10} b^{11})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.2.2.2

Cancel the common factor.

$\frac{6 (a^{4} b)}{6 (9 a^{10} b^{11})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.2.2.3

Rewrite the expression.

$\frac{a^{4} b}{9 a^{10} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.3

Cancel the common factor of $a^{4}$ and $a^{10}$ .

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Step 1.3.1

Factor $a^{4}$ out of $a^{4} b$ .

$\frac{a^{4} (b)}{9 a^{10} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $a^{4}$ out of $9 a^{10} b^{11}$ .

$\frac{a^{4} (b)}{a^{4} (9 a^{6} b^{11})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.3.2.2

Cancel the common factor.

$\frac{a^{4} b}{a^{4} (9 a^{6} b^{11})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.3.2.3

Rewrite the expression.

$\frac{b}{9 a^{6} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.4

Cancel the common factor of $b$ and $b^{11}$ .

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Step 1.4.1

Raise $b$ to the power of $1$ .

$\frac{b^{1}}{9 a^{6} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.4.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot 1}{9 a^{6} b^{11}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.4.3

Cancel the common factors.

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Step 1.4.3.1

Factor $b$ out of $9 a^{6} b^{11}$ .

$\frac{b \cdot 1}{b (9 a^{6} b^{10})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.4.3.2

Cancel the common factor.

$\frac{b \cdot 1}{b (9 a^{6} b^{10})} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 1.4.3.3

Rewrite the expression.

$\frac{1}{9 a^{6} b^{10}} - 12 a^{8} b^{9} + 24 a^{4} b$

Step 2

Move $\frac{1}{9 a^{6} b^{10}}$ .

$- 12 a^{8} b^{9} + 24 a^{4} b + \frac{1}{9 a^{6} b^{10}}$