Simplify (20x^5+15x^2-10x^3)/(5x)

$\frac{20 x^{5} + 15 x^{2} - 10 x^{3}}{5 x}$

Simplify the numerator.

Factor $5 x^{2}$ out of $20 x^{5} + 15 x^{2} - 10 x^{3}$ .

Factor $5 x^{2}$ out of $20 x^{5}$ .

$\frac{5 x^{2} (4 x^{3}) + 15 x^{2} - 10 x^{3}}{5 x}$

Factor $5 x^{2}$ out of $15 x^{2}$ .

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

Factor $5 x^{2}$ out of $- 10 x^{3}$ .

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

Factor $5 x^{2}$ out of $5 x^{2} (4 x^{3}) + 5 x^{2} (3)$ .

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

Factor $5 x^{2}$ out of $5 x^{2} (4 x^{3} + 3) + 5 x^{2} (- 2 x)$ .

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

Reorder terms.

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

Simplify terms.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x (4 x^{3} - 2 x + 3)$ by $1$ .

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$4 x \cdot x^{3} - 2 x \cdot x + x \cdot 3$

Move $3$ to the left of $x$ .

$4 x \cdot x^{3} - 2 x \cdot x + 3 \cdot x$

Simplify each term.

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$4 (x^{3} x^{1}) - 2 x \cdot x + 3 \cdot x$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{3 + 1} - 2 x \cdot x + 3 \cdot x$

Add $3$ and $1$ .

$4 x^{4} - 2 x \cdot x + 3 \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$4 x^{4} - 2 x^{2} + 3 \cdot x$

$4 x^{4} - 2 x^{2} + 3 x$

Simplify (20x^5+15x^2-10x^3)/(5x)

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