Finite Math Examples

$\frac{7 x}{x^{2} \cdot (5 x) - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite using the commutative property of multiplication.

$\frac{7 x}{5 x^{2} x - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 1.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$\frac{7 x}{5 (x \cdot x^{2}) - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 1.2.2

Multiply $x$ by $x^{2}$ .

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Step 1.2.2.1

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

$\frac{7 x}{5 (x^{1} x^{2}) - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 x}{5 x^{1 + 2} - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 1.2.3

Add $1$ and $2$ .

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 x - 6}{14 x^{2}}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 x - 6$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 (x) - 6}{14 x^{2}}$

Step 2.1.2

Factor $3$ out of $- 6$ .

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 x + 3 \cdot - 2}{14 x^{2}}$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 (x - 2)}{14 x^{2}}$

Step 2.2

Cancel the common factor of $7 x$ .

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Step 2.2.1

Factor $7 x$ out of $14 x^{2}$ .

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 (x - 2)}{7 x (2 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{7 x}{5 x^{3} - 14} \cdot \frac{3 (x - 2)}{7 x (2 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{1}{5 x^{3} - 14} \cdot \frac{3 (x - 2)}{2 x}$

Step 2.3

Multiply $\frac{1}{5 x^{3} - 14}$ by $\frac{3 (x - 2)}{2 x}$ .

$\frac{3 (x - 2)}{(5 x^{3} - 14) (2 x)}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Move $2$ to the left of $5 x^{3} - 14$ .

$\frac{3 (x - 2)}{2 \cdot (5 x^{3} - 14) x}$

Step 2.4.2

Reorder factors in $\frac{3 (x - 2)}{2 (5 x^{3} - 14) x}$ .

$\frac{3 (x - 2)}{2 x (5 x^{3} - 14)}$