Simplify (21c^10d^3+56c^6d^2-7c^2d)/(7c^2d)

$\frac{21 c^{10} d^{3} + 56 c^{6} d^{2} - 7 c^{2} d}{7 c^{2} d}$

Step 1

Factor $7 c^{2} d$ out of $21 c^{10} d^{3} + 56 c^{6} d^{2} - 7 c^{2} d$ .

Factor $7 c^{2} d$ out of $21 c^{10} d^{3}$ .

$\frac{7 c^{2} d (3 c^{8} d^{2}) + 56 c^{6} d^{2} - 7 c^{2} d}{7 c^{2} d}$

Factor $7 c^{2} d$ out of $56 c^{6} d^{2}$ .

$\frac{7 c^{2} d (3 c^{8} d^{2}) + 7 c^{2} d (8 c^{4} d) - 7 c^{2} d}{7 c^{2} d}$

Factor $7 c^{2} d$ out of $- 7 c^{2} d$ .

$\frac{7 c^{2} d (3 c^{8} d^{2}) + 7 c^{2} d (8 c^{4} d) + 7 c^{2} d (- 1)}{7 c^{2} d}$

Factor $7 c^{2} d$ out of $7 c^{2} d (3 c^{8} d^{2}) + 7 c^{2} d (8 c^{4} d)$ .

$\frac{7 c^{2} d (3 c^{8} d^{2} + 8 c^{4} d) + 7 c^{2} d (- 1)}{7 c^{2} d}$

Factor $7 c^{2} d$ out of $7 c^{2} d (3 c^{8} d^{2} + 8 c^{4} d) + 7 c^{2} d (- 1)$ .

$\frac{7 c^{2} d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{7 c^{2} d}$

Step 2

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 c^{2} d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{7 c^{2} d}$

Rewrite the expression.

$\frac{c^{2} d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{c^{2} d}$

Step 3

Cancel the common factor of $c^{2}$ .

Cancel the common factor.

$\frac{c^{2} d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{c^{2} d}$

Rewrite the expression.

$\frac{d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{d}$

Step 4

Cancel the common factor of $d$ .

Cancel the common factor.

$\frac{d (3 c^{8} d^{2} + 8 c^{4} d - 1)}{d}$

Divide $3 c^{8} d^{2} + 8 c^{4} d - 1$ by $1$ .

$3 c^{8} d^{2} + 8 c^{4} d - 1$