Simplify (f^2-3f)/f-(3f^2+6f)/(3f)

$\frac{f^{2} - 3 f}{f} - \frac{3 f^{2} + 6 f}{3 f}$

Step 1

Simplify each term.

Factor $f$ out of $f^{2} - 3 f$ .

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

$\frac{f \cdot f - 3 f}{f} - \frac{3 f^{2} + 6 f}{3 f}$

Factor $f$ out of $- 3 f$ .

$\frac{f \cdot f + f \cdot - 3}{f} - \frac{3 f^{2} + 6 f}{3 f}$

Factor $f$ out of $f \cdot f + f \cdot - 3$ .

$\frac{f (f - 3)}{f} - \frac{3 f^{2} + 6 f}{3 f}$

Cancel the common factor of $f$ .

Cancel the common factor.

$\frac{f (f - 3)}{f} - \frac{3 f^{2} + 6 f}{3 f}$

Divide $f - 3$ by $1$ .

$f - 3 - \frac{3 f^{2} + 6 f}{3 f}$

Factor $3 f$ out of $3 f^{2} + 6 f$ .

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

$f - 3 - \frac{3 f (f) + 6 f}{3 f}$

Factor $3 f$ out of $6 f$ .

$f - 3 - \frac{3 f (f) + 3 f (2)}{3 f}$

Factor $3 f$ out of $3 f (f) + 3 f (2)$ .

$f - 3 - \frac{3 f (f + 2)}{3 f}$

Cancel the common factor of $3$ .

Cancel the common factor.

$f - 3 - \frac{3 f (f + 2)}{3 f}$

Rewrite the expression.

$f - 3 - \frac{f (f + 2)}{f}$

Cancel the common factor of $f$ .

Cancel the common factor.

$f - 3 - \frac{f (f + 2)}{f}$

Divide $f + 2$ by $1$ .

$f - 3 - (f + 2)$

Apply the distributive property.

$f - 3 - f - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$f - 3 - f - 2$

Step 2

Simplify by adding terms.

Combine the opposite terms in $f - 3 - f - 2$ .

Subtract $f$ from $f$ .

$0 - 3 - 2$

Subtract $3$ from $0$ .

$- 3 - 2$

Subtract $2$ from $- 3$ .

$- 5$