Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Raise $x$ to the power of $1$ .

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

Step 2.3

Factor $x$ out of $x^{1}$ .

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

Step 2.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

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

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Factor $x + 1$ out of $x (x + 1)$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Raise $x$ to the power of $1$ .

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

Step 4.2

Factor $x$ out of $x^{1}$ .

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

Step 4.3

Cancel the common factors.

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Step 4.3.1

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

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

Step 4.3.2

Cancel the common factor.

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

Step 4.3.3

Rewrite the expression.

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

Step 5

Multiply $2 x - 1$ by $\frac{1}{3 x}$ .

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

Step 6

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

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

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Move the negative in front of the fraction.

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