Simplify ((6c^2+3c)/(-4c+2))/((2c+1)/(4c-2))

$\frac{\frac{6 c^{2} + 3 c}{- 4 c + 2}}{\frac{2 c + 1}{4 c - 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 c^{2} + 3 c}{- 4 c + 2} \cdot \frac{4 c - 2}{2 c + 1}$

Step 2

Factor $3 c$ out of $6 c^{2} + 3 c$ .

Factor $3 c$ out of $6 c^{2}$ .

$\frac{3 c (2 c) + 3 c}{- 4 c + 2} \cdot \frac{4 c - 2}{2 c + 1}$

Factor $3 c$ out of $3 c$ .

$\frac{3 c (2 c) + 3 c (1)}{- 4 c + 2} \cdot \frac{4 c - 2}{2 c + 1}$

Factor $3 c$ out of $3 c (2 c) + 3 c (1)$ .

$\frac{3 c (2 c + 1)}{- 4 c + 2} \cdot \frac{4 c - 2}{2 c + 1}$

Step 3

Factor $2$ out of $- 4 c + 2$ .

Factor $2$ out of $- 4 c$ .

$\frac{3 c (2 c + 1)}{2 (- 2 c) + 2} \cdot \frac{4 c - 2}{2 c + 1}$

Factor $2$ out of $2$ .

$\frac{3 c (2 c + 1)}{2 (- 2 c) + 2 (1)} \cdot \frac{4 c - 2}{2 c + 1}$

Factor $2$ out of $2 (- 2 c) + 2 (1)$ .

$\frac{3 c (2 c + 1)}{2 (- 2 c + 1)} \cdot \frac{4 c - 2}{2 c + 1}$

Step 4

Cancel the common factor of $2 c + 1$ .

Factor $2 c + 1$ out of $3 c (2 c + 1)$ .

$\frac{(2 c + 1) (3 c)}{2 (- 2 c + 1)} \cdot \frac{4 c - 2}{2 c + 1}$

Cancel the common factor.

$\frac{(2 c + 1) (3 c)}{2 (- 2 c + 1)} \cdot \frac{4 c - 2}{2 c + 1}$

Rewrite the expression.

$\frac{3 c}{2 (- 2 c + 1)} (4 c - 2)$

Step 5

Multiply $\frac{3 c}{2 (- 2 c + 1)}$ by $4 c - 2$ .

$\frac{3 c (4 c - 2)}{2 (- 2 c + 1)}$

Step 6

Cancel the common factor of $4 c - 2$ and $2$ .

Factor $2$ out of $3 c (4 c - 2)$ .

$\frac{2 (3 c (2 c - 1))}{2 (- 2 c + 1)}$

Cancel the common factors.

Cancel the common factor.

$\frac{2 (3 c (2 c - 1))}{2 (- 2 c + 1)}$

Rewrite the expression.

$\frac{3 c (2 c - 1)}{- 2 c + 1}$

Step 7

Cancel the common factor of $2 c - 1$ and $- 2 c + 1$ .

Factor $- 1$ out of $2 c$ .

$\frac{3 c (- (- 2 c) - 1)}{- 2 c + 1}$

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{3 c (- (- 2 c) - 1 (1))}{- 2 c + 1}$

Factor $- 1$ out of $- (- 2 c) - 1 (1)$ .

$\frac{3 c (- (- 2 c + 1))}{- 2 c + 1}$

Rewrite $- (- 2 c + 1)$ as $- 1 (- 2 c + 1)$ .

$\frac{3 c (- 1 (- 2 c + 1))}{- 2 c + 1}$

Cancel the common factor.

$\frac{3 c (- 1 (- 2 c + 1))}{- 2 c + 1}$

Divide $3 c \cdot (- 1)$ by $1$ .

$3 c \cdot (- 1)$

Step 8

Multiply $- 1$ by $3$ .

$- 3 c$

Simplify ((6c^2+3c)/(-4c+2))/((2c+1)/(4c-2))

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