Pre-Algebra Examples

$\frac{\frac{(2) (x^{2})}{35}}{\frac{21}{3 x - 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x^{2}}{35} \cdot \frac{3 x - 1}{21}$

Step 2

Multiply $\frac{2 x^{2}}{35} \cdot \frac{3 x - 1}{21}$ .

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Step 2.1

Multiply $\frac{2 x^{2}}{35}$ by $\frac{3 x - 1}{21}$ .

$\frac{2 x^{2} (3 x - 1)}{35 \cdot 21}$

Step 2.2

Multiply $35$ by $21$ .

$\frac{2 x^{2} (3 x - 1)}{735}$

Step 3

Apply the distributive property.

$\frac{2 x^{2} (3 x) + 2 x^{2} \cdot - 1}{735}$

Step 4

Rewrite using the commutative property of multiplication.

$\frac{2 \cdot 3 x^{2} x + 2 x^{2} \cdot - 1}{735}$

Step 5

Multiply $- 1$ by $2$ .

$\frac{2 \cdot 3 x^{2} x - 2 x^{2}}{735}$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $x$ .

$\frac{2 \cdot 3 (x \cdot x^{2}) - 2 x^{2}}{735}$

Step 6.1.2

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

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Step 6.1.2.1

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

$\frac{2 \cdot 3 (x^{1} x^{2}) - 2 x^{2}}{735}$

Step 6.1.2.2

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

$\frac{2 \cdot 3 x^{1 + 2} - 2 x^{2}}{735}$

Step 6.1.3

Add $1$ and $2$ .

$\frac{2 \cdot 3 x^{3} - 2 x^{2}}{735}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{6 x^{3} - 2 x^{2}}{735}$

Step 7

Split the fraction $\frac{6 x^{3} - 2 x^{2}}{735}$ into two fractions.

$\frac{6 x^{3}}{735} + \frac{- 2 x^{2}}{735}$

Step 8

Cancel the common factor of $6$ and $735$ .

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Step 8.1

Factor $3$ out of $6 x^{3}$ .

$\frac{3 (2 x^{3})}{735} + \frac{- 2 x^{2}}{735}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $735$ .

$\frac{3 (2 x^{3})}{3 (245)} + \frac{- 2 x^{2}}{735}$

Step 8.2.2

Cancel the common factor.

$\frac{3 (2 x^{3})}{3 \cdot 245} + \frac{- 2 x^{2}}{735}$

Step 8.2.3

Rewrite the expression.

$\frac{2 x^{3}}{245} + \frac{- 2 x^{2}}{735}$

Step 9

Move the negative in front of the fraction.

$\frac{2 x^{3}}{245} - \frac{2 x^{2}}{735}$