Simplify (9(8-2)-3(15-7))/(6(7-1)-3(17-9))

$\frac{9 (8 - 2) - 3 (15 - 7)}{6 (7 - 1) - 3 (17 - 9)}$

Step 1

Cancel the common factor of $9 (8 - 2) - 3 (15 - 7)$ and $6 (7 - 1) - 3 (17 - 9)$ .

Factor $3$ out of $9 (8 - 2)$ .

$\frac{3 (3 (8 - 2)) - 3 (15 - 7)}{6 (7 - 1) - 3 (17 - 9)}$

Factor $3$ out of $- 3 (15 - 7)$ .

$\frac{3 (3 (8 - 2)) + 3 (- (15 - 7))}{6 (7 - 1) - 3 (17 - 9)}$

Factor $3$ out of $3 (3 (8 - 2)) + 3 (- (15 - 7))$ .

$\frac{3 (3 (8 - 2) - (15 - 7))}{6 (7 - 1) - 3 (17 - 9)}$

Cancel the common factors.

Factor $3$ out of $6 (7 - 1)$ .

$\frac{3 (3 (8 - 2) - (15 - 7))}{3 (2 (7 - 1)) - 3 (17 - 9)}$

Factor $3$ out of $- 3 (17 - 9)$ .

$\frac{3 (3 (8 - 2) - (15 - 7))}{3 (2 (7 - 1)) + 3 (- (17 - 9))}$

Factor $3$ out of $3 (2 (7 - 1)) + 3 (- (17 - 9))$ .

$\frac{3 (3 (8 - 2) - (15 - 7))}{3 (2 (7 - 1) - (17 - 9))}$

Cancel the common factor.

$\frac{3 (3 (8 - 2) - (15 - 7))}{3 (2 (7 - 1) - (17 - 9))}$

Rewrite the expression.

$\frac{3 (8 - 2) - (15 - 7)}{2 (7 - 1) - (17 - 9)}$

Step 2

Simplify the numerator.

Subtract $2$ from $8$ .

$\frac{3 \cdot 6 - (15 - 7)}{2 (7 - 1) - (17 - 9)}$

Multiply $3$ by $6$ .

$\frac{18 - (15 - 7)}{2 (7 - 1) - (17 - 9)}$

Subtract $7$ from $15$ .

$\frac{18 - 1 \cdot 8}{2 (7 - 1) - (17 - 9)}$

Multiply $- 1$ by $8$ .

$\frac{18 - 8}{2 (7 - 1) - (17 - 9)}$

Subtract $8$ from $18$ .

$\frac{10}{2 (7 - 1) - (17 - 9)}$

Step 3

Simplify the denominator.

Subtract $1$ from $7$ .

$\frac{10}{2 \cdot 6 - (17 - 9)}$

Multiply $2$ by $6$ .

$\frac{10}{12 - (17 - 9)}$

Subtract $9$ from $17$ .

$\frac{10}{12 - 1 \cdot 8}$

Multiply $- 1$ by $8$ .

$\frac{10}{12 - 8}$

Subtract $8$ from $12$ .

$\frac{10}{4}$

Step 4

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$\frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$\frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

Simplify (9(8-2)-3(15-7))/(6(7-1)-3(17-9))

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