Finite Math Examples

$\frac{3 x - 3}{x} \cdot \frac{7 x - 7}{9 x^{2}}$

Step 1

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

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 3}{x} \cdot \frac{7 x - 7}{9 x^{2}}$

Step 1.2

Factor $3$ out of $- 3$ .

$\frac{3 (x) + 3 (- 1)}{x} \cdot \frac{7 x - 7}{9 x^{2}}$

Step 1.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\frac{3 (x - 1)}{x} \cdot \frac{7 x - 7}{9 x^{2}}$

Step 2

Factor $7$ out of $7 x - 7$ .

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Step 2.1

Factor $7$ out of $7 x$ .

$\frac{3 (x - 1)}{x} \cdot \frac{7 (x) - 7}{9 x^{2}}$

Step 2.2

Factor $7$ out of $- 7$ .

$\frac{3 (x - 1)}{x} \cdot \frac{7 (x) + 7 (- 1)}{9 x^{2}}$

Step 2.3

Factor $7$ out of $7 (x) + 7 (- 1)$ .

$\frac{3 (x - 1)}{x} \cdot \frac{7 (x - 1)}{9 x^{2}}$

Step 3

Combine.

$\frac{3 (x - 1) (7 (x - 1))}{x (9 x^{2})}$

Step 4

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

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Step 4.1

Move $x^{2}$ .

$\frac{3 (x - 1) (7 (x - 1))}{x^{2} x \cdot 9}$

Step 4.2

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

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Step 4.2.1

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

$\frac{3 (x - 1) (7 (x - 1))}{x^{2} x^{1} \cdot 9}$

Step 4.2.2

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

$\frac{3 (x - 1) (7 (x - 1))}{x^{2 + 1} \cdot 9}$

Step 4.3

Add $2$ and $1$ .

$\frac{3 (x - 1) (7 (x - 1))}{x^{3} \cdot 9}$

Step 5

Cancel the common factor of $3$ and $9$ .

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Step 5.1

Factor $3$ out of $3 (x - 1) (7 (x - 1))$ .

$\frac{3 ((x - 1) (7 (x - 1)))}{x^{3} \cdot 9}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $x^{3} \cdot 9$ .

$\frac{3 ((x - 1) (7 (x - 1)))}{3 (x^{3} \cdot 3)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 ((x - 1) (7 (x - 1)))}{3 (x^{3} \cdot 3)}$

Step 5.2.3

Rewrite the expression.

$\frac{(x - 1) (7 (x - 1))}{x^{3} \cdot 3}$

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{7 ({(x - 1)}^{1} (x - 1))}{x^{3} \cdot 3}$

Step 6.2

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

$\frac{7 ({(x - 1)}^{1} {(x - 1)}^{1})}{x^{3} \cdot 3}$

Step 6.3

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

$\frac{7 {(x - 1)}^{1 + 1}}{x^{3} \cdot 3}$

Step 6.4

Add $1$ and $1$ .

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

Step 7

Move $3$ to the left of $x^{3}$ .

$\frac{7 {(x - 1)}^{2}}{3 x^{3}}$