Finite Math Examples

$\frac{7 x - 7}{3 x + 3} \cdot \frac{10 x + 10}{6 x - 6}$

Step 1

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

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Step 1.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) - 7}{3 x + 3} \cdot \frac{10 x + 10}{6 x - 6}$

Step 1.2

Factor $7$ out of $- 7$ .

$\frac{7 (x) + 7 (- 1)}{3 x + 3} \cdot \frac{10 x + 10}{6 x - 6}$

Step 1.3

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

$\frac{7 (x - 1)}{3 x + 3} \cdot \frac{10 x + 10}{6 x - 6}$

Step 2

Factor $3$ out of $3 x + 3$ .

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{7 (x - 1)}{3 (x) + 3} \cdot \frac{10 x + 10}{6 x - 6}$

Step 2.2

Factor $3$ out of $3$ .

$\frac{7 (x - 1)}{3 (x) + 3 (1)} \cdot \frac{10 x + 10}{6 x - 6}$

Step 2.3

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

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 x + 10}{6 x - 6}$

Step 3

Factor $10$ out of $10 x + 10$ .

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Step 3.1

Factor $10$ out of $10 x$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x) + 10}{6 x - 6}$

Step 3.2

Factor $10$ out of $10$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x) + 10 (1)}{6 x - 6}$

Step 3.3

Factor $10$ out of $10 (x) + 10 (1)$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6 x - 6}$

Step 4

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

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Step 4.1

Factor $6$ out of $6 x$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6 (x) - 6}$

Step 4.2

Factor $6$ out of $- 6$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6 (x) + 6 (- 1)}$

Step 4.3

Factor $6$ out of $6 (x) + 6 (- 1)$ .

$\frac{7 (x - 1)}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6 (x - 1)}$

Step 5

Cancel the common factor of $x - 1$ .

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Step 5.1

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

$\frac{(x - 1) \cdot 7}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6 (x - 1)}$

Step 5.2

Factor $x - 1$ out of $6 (x - 1)$ .

$\frac{(x - 1) \cdot 7}{3 (x + 1)} \cdot \frac{10 (x + 1)}{(x - 1) \cdot 6}$

Step 5.3

Cancel the common factor.

$\frac{(x - 1) \cdot 7}{3 (x + 1)} \cdot \frac{10 (x + 1)}{(x - 1) \cdot 6}$

Step 5.4

Rewrite the expression.

$\frac{7}{3 (x + 1)} \cdot \frac{10 (x + 1)}{6}$

Step 6

Cancel the common factor of $x + 1$ .

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Step 6.1

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

$\frac{7}{(x + 1) \cdot 3} \cdot \frac{10 (x + 1)}{6}$

Step 6.2

Factor $x + 1$ out of $10 (x + 1)$ .

$\frac{7}{(x + 1) \cdot 3} \cdot \frac{(x + 1) \cdot 10}{6}$

Step 6.3

Cancel the common factor.

$\frac{7}{(x + 1) \cdot 3} \cdot \frac{(x + 1) \cdot 10}{6}$

Step 6.4

Rewrite the expression.

$\frac{7}{3} \cdot \frac{10}{6}$

Step 7

Multiply $\frac{7}{3}$ by $\frac{10}{6}$ .

$\frac{7 \cdot 10}{3 \cdot 6}$

Step 8

Multiply.

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Step 8.1

Multiply $7$ by $10$ .

$\frac{70}{3 \cdot 6}$

Step 8.2

Multiply $3$ by $6$ .

$\frac{70}{18}$

Step 9

Cancel the common factor of $70$ and $18$ .

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Step 9.1

Factor $2$ out of $70$ .

$\frac{2 (35)}{18}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 35}{2 \cdot 9}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 35}{2 \cdot 9}$

Step 9.2.3

Rewrite the expression.

$\frac{35}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{9}$

Decimal Form:

$3.\overline{8}$

Mixed Number Form:

$3 \frac{8}{9}$