Algebra Examples

$\frac{4 x^{3} - 3 x^{2}}{2 x}$

Step 1

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

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Step 1.1

Factor $x^{2}$ out of $4 x^{3}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x$ out of $2 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Apply the distributive property.

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

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

$\frac{4 x \cdot x - 3 \cdot x}{2}$

Step 6

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

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x$ .

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

$\frac{4 x^{2} - 3 x}{2}$

Step 7

Split the fraction $\frac{4 x^{2} - 3 x}{2}$ into two fractions.

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

Step 8

Cancel the common factor of $4$ and $2$ .

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 8.2.4

Divide $2 x^{2}$ by $1$ .

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

Step 9

Move the negative in front of the fraction.

$2 x^{2} - \frac{3 x}{2}$