Simplify (4s^3t^2-8st^4+18s^4t^3)/(10s^3t^2)

$\frac{4 s^{3} t^{2} - 8 s t^{4} + 18 s^{4} t^{3}}{10 s^{3} t^{2}}$

Step 1

Factor $2 s t^{2}$ out of $4 s^{3} t^{2} - 8 s t^{4} + 18 s^{4} t^{3}$ .

Factor $2 s t^{2}$ out of $4 s^{3} t^{2}$ .

$\frac{2 s t^{2} (2 s^{2}) - 8 s t^{4} + 18 s^{4} t^{3}}{10 s^{3} t^{2}}$

Factor $2 s t^{2}$ out of $- 8 s t^{4}$ .

$\frac{2 s t^{2} (2 s^{2}) + 2 s t^{2} (- 4 t^{2}) + 18 s^{4} t^{3}}{10 s^{3} t^{2}}$

Factor $2 s t^{2}$ out of $18 s^{4} t^{3}$ .

$\frac{2 s t^{2} (2 s^{2}) + 2 s t^{2} (- 4 t^{2}) + 2 s t^{2} (9 s^{3} t)}{10 s^{3} t^{2}}$

Factor $2 s t^{2}$ out of $2 s t^{2} (2 s^{2}) + 2 s t^{2} (- 4 t^{2})$ .

$\frac{2 s t^{2} (2 s^{2} - 4 t^{2}) + 2 s t^{2} (9 s^{3} t)}{10 s^{3} t^{2}}$

Factor $2 s t^{2}$ out of $2 s t^{2} (2 s^{2} - 4 t^{2}) + 2 s t^{2} (9 s^{3} t)$ .

$\frac{2 s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)}{10 s^{3} t^{2}}$

Step 2

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)$ .

$\frac{2 (s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{10 s^{3} t^{2}}$

Cancel the common factors.

Factor $2$ out of $10 s^{3} t^{2}$ .

$\frac{2 (s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{2 (5 s^{3} t^{2})}$

Cancel the common factor.

$\frac{2 (s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{2 (5 s^{3} t^{2})}$

Rewrite the expression.

$\frac{s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)}{5 s^{3} t^{2}}$

Step 3

Cancel the common factor of $s$ and $s^{3}$ .

Factor $s$ out of $s t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)$ .

$\frac{s (t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{5 s^{3} t^{2}}$

Cancel the common factors.

Factor $s$ out of $5 s^{3} t^{2}$ .

$\frac{s (t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{s (5 s^{2} t^{2})}$

Cancel the common factor.

$\frac{s (t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t))}{s (5 s^{2} t^{2})}$

Rewrite the expression.

$\frac{t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)}{5 s^{2} t^{2}}$

Step 4

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

Cancel the common factor.

$\frac{t^{2} (2 s^{2} - 4 t^{2} + 9 s^{3} t)}{5 s^{2} t^{2}}$

Rewrite the expression.

$\frac{2 s^{2} - 4 t^{2} + 9 s^{3} t}{5 s^{2}}$