Divide (15x^5-25x^3+5x^2)/(5x^4)

$\frac{15 x^{5} - 25 x^{3} + 5 x^{2}}{5 x^{4}}$

Step 1

Factor $5 x^{2}$ out of $15 x^{5} - 25 x^{3} + 5 x^{2}$ .

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

$\frac{5 x^{2} (3 x^{3}) - 25 x^{3} + 5 x^{2}}{5 x^{4}}$

Factor $5 x^{2}$ out of $- 25 x^{3}$ .

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

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

$\frac{5 x^{2} (3 x^{3}) + 5 x^{2} (- 5 x) + 5 x^{2} (1)}{5 x^{4}}$

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

$\frac{5 x^{2} (3 x^{3} - 5 x) + 5 x^{2} (1)}{5 x^{4}}$

Factor $5 x^{2}$ out of $5 x^{2} (3 x^{3} - 5 x) + 5 x^{2} (1)$ .

$\frac{5 x^{2} (3 x^{3} - 5 x + 1)}{5 x^{4}}$

Step 2

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2} (3 x^{3} - 5 x + 1)}{5 x^{4}}$

Rewrite the expression.

$\frac{x^{2} (3 x^{3} - 5 x + 1)}{x^{4}}$

Step 3

Cancel the common factors.

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

$\frac{x^{2} (3 x^{3} - 5 x + 1)}{x^{2} x^{2}}$

Cancel the common factor.

$\frac{x^{2} (3 x^{3} - 5 x + 1)}{x^{2} x^{2}}$

Rewrite the expression.

$\frac{3 x^{3} - 5 x + 1}{x^{2}}$

Step 4

Split the fraction $\frac{3 x^{3} - 5 x + 1}{x^{2}}$ into two fractions.

$\frac{3 x^{3} - 5 x}{x^{2}} + \frac{1}{x^{2}}$

Step 5

Split the fraction $\frac{3 x^{3} - 5 x}{x^{2}}$ into two fractions.

$\frac{3 x^{3}}{x^{2}} + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Step 6

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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

$\frac{x^{2} (3 x)}{x^{2}} + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{2} (3 x)}{x^{2} \cdot 1} + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Cancel the common factor.

$\frac{x^{2} (3 x)}{x^{2} \cdot 1} + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Rewrite the expression.

$\frac{3 x}{1} + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Divide $3 x$ by $1$ .

$3 x + \frac{- 5 x}{x^{2}} + \frac{1}{x^{2}}$

Step 7

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

Factor $x$ out of $- 5 x$ .

$3 x + \frac{x \cdot - 5}{x^{2}} + \frac{1}{x^{2}}$

Cancel the common factors.

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

$3 x + \frac{x \cdot - 5}{x \cdot x} + \frac{1}{x^{2}}$

Cancel the common factor.

$3 x + \frac{x \cdot - 5}{x \cdot x} + \frac{1}{x^{2}}$

Rewrite the expression.

$3 x + \frac{- 5}{x} + \frac{1}{x^{2}}$

Step 8

Move the negative in front of the fraction.

$3 x - \frac{5}{x} + \frac{1}{x^{2}}$

Divide (15x^5-25x^3+5x^2)/(5x^4)

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