Pre-Algebra Examples

$\frac{2 x - 3}{x} \div \frac{7}{x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x - 3}{x} \cdot \frac{x^{2}}{7}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

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

$\frac{2 x - 3}{x} \cdot \frac{x \cdot x}{7}$

Step 2.2

Cancel the common factor.

$\frac{2 x - 3}{x} \cdot \frac{x \cdot x}{7}$

Step 2.3

Rewrite the expression.

$(2 x - 3) \frac{x}{7}$

Step 3

Apply the distributive property.

$2 x \frac{x}{7} - 3 \frac{x}{7}$

Step 4

Multiply $2 x \frac{x}{7}$ .

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Step 4.1

Combine $2$ and $\frac{x}{7}$ .

$x \frac{2 x}{7} - 3 \frac{x}{7}$

Step 4.2

Combine $x$ and $\frac{2 x}{7}$ .

$\frac{x (2 x)}{7} - 3 \frac{x}{7}$

Step 4.3

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

$\frac{2 (x^{1} x)}{7} - 3 \frac{x}{7}$

Step 4.4

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

$\frac{2 (x^{1} x^{1})}{7} - 3 \frac{x}{7}$

Step 4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x^{1 + 1}}{7} - 3 \frac{x}{7}$

Step 4.6

Add $1$ and $1$ .

$\frac{2 x^{2}}{7} - 3 \frac{x}{7}$

Step 5

Combine $- 3$ and $\frac{x}{7}$ .

$\frac{2 x^{2}}{7} + \frac{- 3 x}{7}$

Step 6

Combine the numerators over the common denominator.

$\frac{2 x^{2} - 3 x}{7}$

Step 7

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

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Step 7.1

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

$\frac{x (2 x) - 3 x}{7}$

Step 7.2

Factor $x$ out of $- 3 x$ .

$\frac{x (2 x) + x \cdot - 3}{7}$

Step 7.3

Factor $x$ out of $x (2 x) + x \cdot - 3$ .

$\frac{x (2 x - 3)}{7}$