Simplify (3x^3-15x^2+15x-75)/(3x^2+15)

$\frac{3 x^{3} - 15 x^{2} + 15 x - 75}{3 x^{2} + 15}$

Step 1

Cancel the common factor of $3 x^{3} - 15 x^{2} + 15 x - 75$ and $3 x^{2} + 15$ .

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

$\frac{3 (x^{3}) - 15 x^{2} + 15 x - 75}{3 x^{2} + 15}$

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

$\frac{3 (x^{3}) + 3 (- 5 x^{2}) + 15 x - 75}{3 x^{2} + 15}$

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

$\frac{3 (x^{3} - 5 x^{2}) + 15 x - 75}{3 x^{2} + 15}$

Factor $3$ out of $15 x$ .

$\frac{3 (x^{3} - 5 x^{2}) + 3 (5 x) - 75}{3 x^{2} + 15}$

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

$\frac{3 (x^{3} - 5 x^{2} + 5 x) - 75}{3 x^{2} + 15}$

Factor $3$ out of $- 75$ .

$\frac{3 (x^{3} - 5 x^{2} + 5 x) + 3 \cdot - 25}{3 x^{2} + 15}$

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

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

Cancel the common factors.

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

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

Factor $3$ out of $15$ .

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

Factor $3$ out of $3 x^{2} + 3 \cdot 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $x - 5$ .

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

Step 3

Cancel the common factor of $x^{2} + 5$ .

Cancel the common factor.

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

Divide $x - 5$ by $1$ .

$x - 5$