Simplify (4x+36)/(5x-5)*(9x-9)/(6x+54)

$\frac{4 x + 36}{5 x - 5} \cdot \frac{9 x - 9}{6 x + 54}$

Step 1

Factor $4$ out of $4 x + 36$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 36}{5 x - 5} \cdot \frac{9 x - 9}{6 x + 54}$

Factor $4$ out of $36$ .

$\frac{4 x + 4 \cdot 9}{5 x - 5} \cdot \frac{9 x - 9}{6 x + 54}$

Factor $4$ out of $4 x + 4 \cdot 9$ .

$\frac{4 (x + 9)}{5 x - 5} \cdot \frac{9 x - 9}{6 x + 54}$

Step 2

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

Factor $5$ out of $5 x$ .

$\frac{4 (x + 9)}{5 (x) - 5} \cdot \frac{9 x - 9}{6 x + 54}$

Factor $5$ out of $- 5$ .

$\frac{4 (x + 9)}{5 (x) + 5 (- 1)} \cdot \frac{9 x - 9}{6 x + 54}$

Factor $5$ out of $5 (x) + 5 (- 1)$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 x - 9}{6 x + 54}$

Step 3

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

Factor $9$ out of $9 x$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x) - 9}{6 x + 54}$

Factor $9$ out of $- 9$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x) + 9 (- 1)}{6 x + 54}$

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{6 x + 54}$

Step 4

Factor $6$ out of $6 x + 54$ .

Factor $6$ out of $6 x$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{6 (x) + 54}$

Factor $6$ out of $54$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{6 x + 6 \cdot 9}$

Factor $6$ out of $6 x + 6 \cdot 9$ .

$\frac{4 (x + 9)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{6 (x + 9)}$

Step 5

Cancel the common factor of $2 (x + 9)$ .

Factor $2 (x + 9)$ out of $4 (x + 9)$ .

$\frac{2 (x + 9) (2)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{6 (x + 9)}$

Factor $2 (x + 9)$ out of $6 (x + 9)$ .

$\frac{2 (x + 9) (2)}{5 (x - 1)} \cdot \frac{9 (x - 1)}{2 (x + 9) (3)}$

Cancel the common factor.

$\frac{2 (x + 9) \cdot 2}{5 (x - 1)} \cdot \frac{9 (x - 1)}{2 (x + 9) \cdot 3}$

Rewrite the expression.

$\frac{2}{5 (x - 1)} \cdot \frac{9 (x - 1)}{3}$

Step 6

Cancel the common factor of $x - 1$ .

Factor $x - 1$ out of $5 (x - 1)$ .

$\frac{2}{(x - 1) \cdot 5} \cdot \frac{9 (x - 1)}{3}$

Factor $x - 1$ out of $9 (x - 1)$ .

$\frac{2}{(x - 1) \cdot 5} \cdot \frac{(x - 1) \cdot 9}{3}$

Cancel the common factor.

$\frac{2}{(x - 1) \cdot 5} \cdot \frac{(x - 1) \cdot 9}{3}$

Rewrite the expression.

$\frac{2}{5} \cdot \frac{9}{3}$

Step 7

Multiply $\frac{2}{5}$ by $\frac{9}{3}$ .

$\frac{2 \cdot 9}{5 \cdot 3}$

Step 8

Multiply.

Multiply $2$ by $9$ .

$\frac{18}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{18}{15}$

Step 9

Cancel the common factor of $18$ and $15$ .

Factor $3$ out of $18$ .

$\frac{3 (6)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$\frac{3 \cdot 6}{3 \cdot 5}$

Cancel the common factor.

$\frac{3 \cdot 6}{3 \cdot 5}$

Rewrite the expression.

$\frac{6}{5}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{5}$

Decimal Form:

$1.2$

Mixed Number Form:

$1 \frac{1}{5}$

Simplify (4x+36)/(5x-5)*(9x-9)/(6x+54)

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