Simplify (9!-6!+4!)/(4!+7!)

$\frac{9! - 6! + 4!}{4! + 7!}$

Step 1

Simplify the numerator.

Expand $9!$ to $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $9$ by $8$ .

$\frac{72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $72$ by $7$ .

$\frac{504 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $504$ by $6$ .

$\frac{3024 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $3024$ by $5$ .

$\frac{15120 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $15120$ by $4$ .

$\frac{60480 \cdot 3 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $60480$ by $3$ .

$\frac{181440 \cdot 2 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $181440$ by $2$ .

$\frac{362880 \cdot 1 - 6! + 4!}{4! + 7!}$

Multiply $362880$ by $1$ .

$\frac{362880 - 6! + 4!}{4! + 7!}$

Expand $6!$ to $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{362880 - (6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1) + 4!}{4! + 7!}$

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $6$ by $5$ .

$\frac{362880 - (30 \cdot 4 \cdot 3 \cdot 2 \cdot 1) + 4!}{4! + 7!}$

Multiply $30$ by $4$ .

$\frac{362880 - (120 \cdot 3 \cdot 2 \cdot 1) + 4!}{4! + 7!}$

Multiply $120$ by $3$ .

$\frac{362880 - (360 \cdot 2 \cdot 1) + 4!}{4! + 7!}$

Multiply $360$ by $2$ .

$\frac{362880 - (720 \cdot 1) + 4!}{4! + 7!}$

Multiply $720$ by $1$ .

$\frac{362880 - 1 \cdot 720 + 4!}{4! + 7!}$

Multiply $- 1$ by $720$ .

$\frac{362880 - 720 + 4!}{4! + 7!}$

Expand $4!$ to $4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{362880 - 720 + 4 \cdot 3 \cdot 2 \cdot 1}{4! + 7!}$

Multiply $4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $4$ by $3$ .

$\frac{362880 - 720 + 12 \cdot 2 \cdot 1}{4! + 7!}$

Multiply $12$ by $2$ .

$\frac{362880 - 720 + 24 \cdot 1}{4! + 7!}$

Multiply $24$ by $1$ .

$\frac{362880 - 720 + 24}{4! + 7!}$

Subtract $720$ from $362880$ .

$\frac{362160 + 24}{4! + 7!}$

Add $362160$ and $24$ .

$\frac{362184}{4! + 7!}$

Step 2

Simplify the denominator.

Expand $4!$ to $4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{362184}{4 \cdot 3 \cdot 2 \cdot 1 + 7!}$

Multiply $4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $4$ by $3$ .

$\frac{362184}{12 \cdot 2 \cdot 1 + 7!}$

Multiply $12$ by $2$ .

$\frac{362184}{24 \cdot 1 + 7!}$

Multiply $24$ by $1$ .

$\frac{362184}{24 + 7!}$

Expand $7!$ to $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{362184}{24 + 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Multiply $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $7$ by $6$ .

$\frac{362184}{24 + 42 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Multiply $42$ by $5$ .

$\frac{362184}{24 + 210 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Multiply $210$ by $4$ .

$\frac{362184}{24 + 840 \cdot 3 \cdot 2 \cdot 1}$

Multiply $840$ by $3$ .

$\frac{362184}{24 + 2520 \cdot 2 \cdot 1}$

Multiply $2520$ by $2$ .

$\frac{362184}{24 + 5040 \cdot 1}$

Multiply $5040$ by $1$ .

$\frac{362184}{24 + 5040}$

Add $24$ and $5040$ .

$\frac{362184}{5064}$

Step 3

Cancel the common factor of $362184$ and $5064$ .

Factor $24$ out of $362184$ .

$\frac{24 (15091)}{5064}$

Cancel the common factors.

Factor $24$ out of $5064$ .

$\frac{24 \cdot 15091}{24 \cdot 211}$

Cancel the common factor.

$\frac{24 \cdot 15091}{24 \cdot 211}$

Rewrite the expression.

$\frac{15091}{211}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{15091}{211}$

Decimal Form:

$71.52132701 \dots$

Mixed Number Form:

$71 \frac{110}{211}$

Simplify (9!-6!+4!)/(4!+7!)

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