Algebra Examples

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

Step 1

Divide each term in $f (- x) = 3 x^{2} + 2 x - 4$ by $- x$ .

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

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Dividing two negative values results in a positive value.

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

Step 2.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\frac{f x}{x} = \frac{3 x^{2}}{- x} + \frac{2 x}{- x} + \frac{- 4}{- x}$

Step 2.2.2

Divide $f$ by $1$ .

$f = \frac{3 x^{2}}{- x} + \frac{2 x}{- x} + \frac{- 4}{- x}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

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

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

Step 3.1.1.2

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

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

Step 3.1.2

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

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

Step 3.1.3

Multiply $3$ by $- 1$ .

$f = - 3 x + \frac{2 x}{- x} + \frac{- 4}{- x}$

Step 3.1.4

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.4.1

Cancel the common factor.

$f = - 3 x + \frac{2 x}{- x} + \frac{- 4}{- x}$

Step 3.1.4.2

Rewrite the expression.

$f = - 3 x + \frac{2}{- 1} + \frac{- 4}{- x}$

Step 3.1.4.3

Move the negative one from the denominator of $\frac{2}{- 1}$ .

$f = - 3 x - 1 \cdot 2 + \frac{- 4}{- x}$

Step 3.1.5

Multiply $- 1$ by $2$ .

$f = - 3 x - 2 + \frac{- 4}{- x}$

Step 3.1.6

Dividing two negative values results in a positive value.

$f = - 3 x - 2 + \frac{4}{x}$