Basic Math Examples

$\frac{(84 a^{2} b^{5} c^{7}) - 2}{(48 a^{5} b^{- 3} c^{2}) - 2}$

Step 1

Cancel the common factor of $(84 a^{2} b^{5} c^{7}) - 2$ and $(48 a^{5} b^{- 3} c^{2}) - 2$ .

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Step 1.1

Factor $2$ out of $84 a^{2} b^{5} c^{7}$ .

$\frac{2 (42 a^{2} b^{5} c^{7}) - 2}{(48 a^{5} b^{- 3} c^{2}) - 2}$

Step 1.2

Factor $2$ out of $- 2$ .

$\frac{2 (42 a^{2} b^{5} c^{7}) + 2 (- 1)}{(48 a^{5} b^{- 3} c^{2}) - 2}$

Step 1.3

Factor $2$ out of $2 (42 a^{2} b^{5} c^{7}) + 2 (- 1)$ .

$\frac{2 (42 a^{2} b^{5} c^{7} - 1)}{(48 a^{5} b^{- 3} c^{2}) - 2}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $48 a^{5} b^{- 3} c^{2}$ .

$\frac{2 (42 a^{2} b^{5} c^{7} - 1)}{2 (24 a^{5} b^{- 3} c^{2}) - 2}$

Step 1.4.2

Factor $2$ out of $- 2$ .

$\frac{2 (42 a^{2} b^{5} c^{7} - 1)}{2 (24 a^{5} b^{- 3} c^{2}) + 2 (- 1)}$

Step 1.4.3

Factor $2$ out of $2 (24 a^{5} b^{- 3} c^{2}) + 2 (- 1)$ .

$\frac{2 (42 a^{2} b^{5} c^{7} - 1)}{2 (24 a^{5} b^{- 3} c^{2} - 1)}$

Step 1.4.4

Cancel the common factor.

$\frac{2 (42 a^{2} b^{5} c^{7} - 1)}{2 (24 a^{5} b^{- 3} c^{2} - 1)}$

Step 1.4.5

Rewrite the expression.

$\frac{42 a^{2} b^{5} c^{7} - 1}{24 a^{5} b^{- 3} c^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{24 a^{5} \frac{1}{b^{3}} c^{2} - 1}$

Step 2.2

Multiply $24 a^{5} \frac{1}{b^{3}}$ .

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Step 2.2.1

Combine $24$ and $\frac{1}{b^{3}}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{a^{5} \frac{24}{b^{3}} c^{2} - 1}$

Step 2.2.2

Combine $a^{5}$ and $\frac{24}{b^{3}}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{a^{5} \cdot 24}{b^{3}} c^{2} - 1}$

Step 2.3

Move $24$ to the left of $a^{5}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{24 \cdot a^{5}}{b^{3}} c^{2} - 1}$

Step 2.4

Combine $\frac{24 a^{5}}{b^{3}}$ and $c^{2}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{24 a^{5} c^{2}}{b^{3}} - 1}$

Step 2.5

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{b^{3}}{b^{3}}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{24 a^{5} c^{2}}{b^{3}} - 1 \cdot \frac{b^{3}}{b^{3}}}$

Step 2.6

Combine $- 1$ and $\frac{b^{3}}{b^{3}}$ .

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{24 a^{5} c^{2}}{b^{3}} + \frac{- b^{3}}{b^{3}}}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{42 a^{2} b^{5} c^{7} - 1}{\frac{24 a^{5} c^{2} - b^{3}}{b^{3}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$(42 a^{2} b^{5} c^{7} - 1) \frac{b^{3}}{24 a^{5} c^{2} - b^{3}}$

Step 4

Multiply $42 a^{2} b^{5} c^{7} - 1$ by $\frac{b^{3}}{24 a^{5} c^{2} - b^{3}}$ .

$\frac{(42 a^{2} b^{5} c^{7} - 1) b^{3}}{24 a^{5} c^{2} - b^{3}}$

Step 5

Reorder factors in $\frac{(42 a^{2} b^{5} c^{7} - 1) b^{3}}{24 a^{5} c^{2} - b^{3}}$ .

$\frac{b^{3} (42 a^{2} b^{5} c^{7} - 1)}{24 a^{5} c^{2} - b^{3}}$