Simplify ((18x-6)/(9x^5))/((15x+5)/(21x^2))

$\frac{\frac{18 x - 6}{9 x^{5}}}{\frac{15 x + 5}{21 x^{2}}}$

Step 1

Cancel the common factor of $18 x - 6$ and $9$ .

Factor $3$ out of $18 x$ .

$\frac{\frac{3 (6 x) - 6}{9 x^{5}}}{\frac{15 x + 5}{21 x^{2}}}$

Factor $3$ out of $- 6$ .

$\frac{\frac{3 (6 x) + 3 (- 2)}{9 x^{5}}}{\frac{15 x + 5}{21 x^{2}}}$

Factor $3$ out of $3 (6 x) + 3 (- 2)$ .

$\frac{\frac{3 (6 x - 2)}{9 x^{5}}}{\frac{15 x + 5}{21 x^{2}}}$

Cancel the common factors.

Factor $3$ out of $9 x^{5}$ .

$\frac{\frac{3 (6 x - 2)}{3 (3 x^{5})}}{\frac{15 x + 5}{21 x^{2}}}$

Cancel the common factor.

$\frac{\frac{3 (6 x - 2)}{3 (3 x^{5})}}{\frac{15 x + 5}{21 x^{2}}}$

Rewrite the expression.

$\frac{\frac{6 x - 2}{3 x^{5}}}{\frac{15 x + 5}{21 x^{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 x - 2}{3 x^{5}} \cdot \frac{21 x^{2}}{15 x + 5}$

Step 3

Simplify terms.

Cancel the common factor of $3 x^{2}$ .

Factor $3 x^{2}$ out of $3 x^{5}$ .

$\frac{6 x - 2}{3 x^{2} (x^{3})} \cdot \frac{21 x^{2}}{15 x + 5}$

Factor $3 x^{2}$ out of $21 x^{2}$ .

$\frac{6 x - 2}{3 x^{2} (x^{3})} \cdot \frac{3 x^{2} (7)}{15 x + 5}$

Cancel the common factor.

$\frac{6 x - 2}{3 x^{2} x^{3}} \cdot \frac{3 x^{2} \cdot 7}{15 x + 5}$

Rewrite the expression.

$\frac{6 x - 2}{x^{3}} \cdot \frac{7}{15 x + 5}$

Multiply $\frac{6 x - 2}{x^{3}}$ by $\frac{7}{15 x + 5}$ .

$\frac{(6 x - 2) \cdot 7}{x^{3} (15 x + 5)}$

Step 4

Simplify the numerator.

Factor $2$ out of $6 x - 2$ .

Factor $2$ out of $6 x$ .

$\frac{(2 (3 x) - 2) \cdot 7}{x^{3} (15 x + 5)}$

Factor $2$ out of $- 2$ .

$\frac{(2 (3 x) + 2 (- 1)) \cdot 7}{x^{3} (15 x + 5)}$

Factor $2$ out of $2 (3 x) + 2 (- 1)$ .

$\frac{2 (3 x - 1) \cdot 7}{x^{3} (15 x + 5)}$

Multiply $7$ by $2$ .

$\frac{14 (3 x - 1)}{x^{3} (15 x + 5)}$

Step 5

Factor $5$ out of $15 x + 5$ .

Factor $5$ out of $15 x$ .

$\frac{14 (3 x - 1)}{x^{3} (5 (3 x) + 5)}$

Factor $5$ out of $5$ .

$\frac{14 (3 x - 1)}{x^{3} (5 (3 x) + 5 (1))}$

Factor $5$ out of $5 (3 x) + 5 (1)$ .

$\frac{14 (3 x - 1)}{x^{3} (5 (3 x + 1))}$

$\frac{14 (3 x - 1)}{x^{3} \cdot 5 (3 x + 1)}$

Step 6

Move $5$ to the left of $x^{3}$ .

$\frac{14 (3 x - 1)}{5 x^{3} (3 x + 1)}$

Simplify ((18x-6)/(9x^5))/((15x+5)/(21x^2))

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