Simplify (6x+24)/(5x-35)*(9x-63)/(7x+28)

$\frac{6 x + 24}{5 x - 35} \cdot \frac{9 x - 63}{7 x + 28}$

Step 1

Factor $6$ out of $6 x + 24$ .

Factor $6$ out of $6 x$ .

$\frac{6 (x) + 24}{5 x - 35} \cdot \frac{9 x - 63}{7 x + 28}$

Factor $6$ out of $24$ .

$\frac{6 x + 6 \cdot 4}{5 x - 35} \cdot \frac{9 x - 63}{7 x + 28}$

Factor $6$ out of $6 x + 6 \cdot 4$ .

$\frac{6 (x + 4)}{5 x - 35} \cdot \frac{9 x - 63}{7 x + 28}$

Step 2

Factor $5$ out of $5 x - 35$ .

Factor $5$ out of $5 x$ .

$\frac{6 (x + 4)}{5 (x) - 35} \cdot \frac{9 x - 63}{7 x + 28}$

Factor $5$ out of $- 35$ .

$\frac{6 (x + 4)}{5 x + 5 \cdot - 7} \cdot \frac{9 x - 63}{7 x + 28}$

Factor $5$ out of $5 x + 5 \cdot - 7$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 x - 63}{7 x + 28}$

Step 3

Factor $9$ out of $9 x - 63$ .

Factor $9$ out of $9 x$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 (x) - 63}{7 x + 28}$

Factor $9$ out of $- 63$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 x + 9 \cdot - 7}{7 x + 28}$

Factor $9$ out of $9 x + 9 \cdot - 7$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7 x + 28}$

Step 4

Factor $7$ out of $7 x + 28$ .

Factor $7$ out of $7 x$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7 (x) + 28}$

Factor $7$ out of $28$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7 x + 7 \cdot 4}$

Factor $7$ out of $7 x + 7 \cdot 4$ .

$\frac{6 (x + 4)}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7 (x + 4)}$

Step 5

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $6 (x + 4)$ .

$\frac{(x + 4) \cdot 6}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7 (x + 4)}$

Factor $x + 4$ out of $7 (x + 4)$ .

$\frac{(x + 4) \cdot 6}{5 (x - 7)} \cdot \frac{9 (x - 7)}{(x + 4) \cdot 7}$

Cancel the common factor.

$\frac{(x + 4) \cdot 6}{5 (x - 7)} \cdot \frac{9 (x - 7)}{(x + 4) \cdot 7}$

Rewrite the expression.

$\frac{6}{5 (x - 7)} \cdot \frac{9 (x - 7)}{7}$

Step 6

Cancel the common factor of $x - 7$ .

Factor $x - 7$ out of $5 (x - 7)$ .

$\frac{6}{(x - 7) \cdot 5} \cdot \frac{9 (x - 7)}{7}$

Factor $x - 7$ out of $9 (x - 7)$ .

$\frac{6}{(x - 7) \cdot 5} \cdot \frac{(x - 7) \cdot 9}{7}$

Cancel the common factor.

$\frac{6}{(x - 7) \cdot 5} \cdot \frac{(x - 7) \cdot 9}{7}$

Rewrite the expression.

$\frac{6}{5} \cdot \frac{9}{7}$

Step 7

Multiply $\frac{6}{5}$ by $\frac{9}{7}$ .

$\frac{6 \cdot 9}{5 \cdot 7}$

Step 8

Multiply.

Multiply $6$ by $9$ .

$\frac{54}{5 \cdot 7}$

Multiply $5$ by $7$ .

$\frac{54}{35}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{54}{35}$

Decimal Form:

$1.54285714 \dots$

Mixed Number Form:

$1 \frac{19}{35}$

Simplify (6x+24)/(5x-35)*(9x-63)/(7x+28)

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