Pre-Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Combine.

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

Step 4

Multiply $7$ by $1$ .

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

Step 5

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 5.1

Multiply $x^{2}$ by $x$ .

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Step 5.1.1

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

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

Step 5.1.2

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

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

Step 5.2

Add $2$ and $1$ .

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

Step 6

Multiply $2 x - 3$ by $\frac{7}{x^{3}}$ .

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

Step 7

Move $7$ to the left of $2 x - 3$ .

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

Step 8

Apply the distributive property.

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

Step 9

Multiply $2$ by $7$ .

$\frac{14 x + 7 \cdot - 3}{x^{3}}$

Step 10

Multiply $7$ by $- 3$ .

$\frac{14 x - 21}{x^{3}}$

Step 11

Split the fraction $\frac{14 x - 21}{x^{3}}$ into two fractions.

$\frac{14 x}{x^{3}} + \frac{- 21}{x^{3}}$

Step 12

Cancel the common factor of $x$ and $x^{3}$ .

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Step 12.1

Factor $x$ out of $14 x$ .

$\frac{x \cdot 14}{x^{3}} + \frac{- 21}{x^{3}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

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

$\frac{x \cdot 14}{x \cdot x^{2}} + \frac{- 21}{x^{3}}$

Step 12.2.2

Cancel the common factor.

$\frac{x \cdot 14}{x \cdot x^{2}} + \frac{- 21}{x^{3}}$

Step 12.2.3

Rewrite the expression.

$\frac{14}{x^{2}} + \frac{- 21}{x^{3}}$

Step 13

Move the negative in front of the fraction.

$\frac{14}{x^{2}} - \frac{21}{x^{3}}$