Simplify ((6x+9)/(15x^2))/((16x-12)/(10x^4))

$\frac{\frac{6 x + 9}{15 x^{2}}}{\frac{16 x - 12}{10 x^{4}}}$

Step 1

Cancel the common factor of $6 x + 9$ and $15$ .

Factor $3$ out of $6 x$ .

$\frac{\frac{3 (2 x) + 9}{15 x^{2}}}{\frac{16 x - 12}{10 x^{4}}}$

Factor $3$ out of $9$ .

$\frac{\frac{3 (2 x) + 3 (3)}{15 x^{2}}}{\frac{16 x - 12}{10 x^{4}}}$

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

$\frac{\frac{3 (2 x + 3)}{15 x^{2}}}{\frac{16 x - 12}{10 x^{4}}}$

Cancel the common factors.

Factor $3$ out of $15 x^{2}$ .

$\frac{\frac{3 (2 x + 3)}{3 (5 x^{2})}}{\frac{16 x - 12}{10 x^{4}}}$

Cancel the common factor.

$\frac{\frac{3 (2 x + 3)}{3 (5 x^{2})}}{\frac{16 x - 12}{10 x^{4}}}$

Rewrite the expression.

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{16 x - 12}{10 x^{4}}}$

Step 2

Cancel the common factor of $16 x - 12$ and $10$ .

Factor $2$ out of $16 x$ .

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{2 (8 x) - 12}{10 x^{4}}}$

Factor $2$ out of $- 12$ .

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{2 (8 x) + 2 (- 6)}{10 x^{4}}}$

Factor $2$ out of $2 (8 x) + 2 (- 6)$ .

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{2 (8 x - 6)}{10 x^{4}}}$

Cancel the common factors.

Factor $2$ out of $10 x^{4}$ .

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{2 (8 x - 6)}{2 (5 x^{4})}}$

Cancel the common factor.

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{2 (8 x - 6)}{2 (5 x^{4})}}$

Rewrite the expression.

$\frac{\frac{2 x + 3}{5 x^{2}}}{\frac{8 x - 6}{5 x^{4}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x + 3}{5 x^{2}} \cdot \frac{5 x^{4}}{8 x - 6}$

Step 4

Cancel the common factor of $5 x^{2}$ .

Factor $5 x^{2}$ out of $5 x^{4}$ .

$\frac{2 x + 3}{5 x^{2}} \cdot \frac{5 x^{2} (x^{2})}{8 x - 6}$

Cancel the common factor.

$\frac{2 x + 3}{5 x^{2}} \cdot \frac{5 x^{2} x^{2}}{8 x - 6}$

Rewrite the expression.

$(2 x + 3) \frac{x^{2}}{8 x - 6}$

Step 5

Factor $2$ out of $8 x - 6$ .

Factor $2$ out of $8 x$ .

$(2 x + 3) \frac{x^{2}}{2 (4 x) - 6}$

Factor $2$ out of $- 6$ .

$(2 x + 3) \frac{x^{2}}{2 (4 x) + 2 (- 3)}$

Factor $2$ out of $2 (4 x) + 2 (- 3)$ .

$(2 x + 3) \frac{x^{2}}{2 (4 x - 3)}$

Step 6

Multiply $2 x + 3$ by $\frac{x^{2}}{2 (4 x - 3)}$ .

$\frac{(2 x + 3) x^{2}}{2 (4 x - 3)}$

Step 7

Reorder factors in $\frac{(2 x + 3) x^{2}}{2 (4 x - 3)}$ .

$\frac{x^{2} (2 x + 3)}{2 (4 x - 3)}$

Simplify ((6x+9)/(15x^2))/((16x-12)/(10x^4))

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