Pre-Algebra Examples

$\frac{(35 x^{2} - 25 x) + 45}{5 x^{\frac{2}{3}}}$

Step 1

Factor $5$ out of $35 x^{2}$ .

$\frac{5 (7 x^{2}) - 25 x + 45}{5 x^{\frac{2}{3}}}$

Step 2

Factor $5$ out of $- 25 x$ .

$\frac{5 (7 x^{2}) + 5 (- 5 x) + 45}{5 x^{\frac{2}{3}}}$

Step 3

Factor $5$ out of $5 (7 x^{2}) + 5 (- 5 x)$ .

$\frac{5 (7 x^{2} - 5 x) + 45}{5 x^{\frac{2}{3}}}$

Step 4

Factor $5$ out of $45$ .

$\frac{5 (7 x^{2} - 5 x) + 5 \cdot 9}{5 x^{\frac{2}{3}}}$

Step 5

Factor $5$ out of $5 (7 x^{2} - 5 x) + 5 (9)$ .

$\frac{5 (7 x^{2} - 5 x + 9)}{5 x^{\frac{2}{3}}}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $5$ out of $5 x^{\frac{2}{3}}$ .

$\frac{5 (7 x^{2} - 5 x + 9)}{5 (x^{\frac{2}{3}})}$

Step 6.2

Cancel the common factor.

$\frac{5 (7 x^{2} - 5 x + 9)}{5 x^{\frac{2}{3}}}$

Step 6.3

Rewrite the expression.

$\frac{7 x^{2} - 5 x + 9}{x^{\frac{2}{3}}}$

Step 7

Split the fraction $\frac{7 x^{2} - 5 x + 9}{x^{\frac{2}{3}}}$ into two fractions.

$\frac{7 x^{2} - 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 8

Split the fraction $\frac{7 x^{2} - 5 x}{x^{\frac{2}{3}}}$ into two fractions.

$\frac{7 x^{2}}{x^{\frac{2}{3}}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 9

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$7 x^{2} x^{- \frac{2}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10

Multiply $x^{2}$ by $x^{- \frac{2}{3}}$ by adding the exponents.

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Step 10.1

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

$7 (x^{- \frac{2}{3}} x^{2}) + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.2

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

$7 x^{- \frac{2}{3} + 2} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7 x^{- \frac{2}{3} + 2 \cdot \frac{3}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.4

Combine $2$ and $\frac{3}{3}$ .

$7 x^{- \frac{2}{3} + \frac{2 \cdot 3}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.5

Combine the numerators over the common denominator.

$7 x^{\frac{- 2 + 2 \cdot 3}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.6

Simplify the numerator.

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Step 10.6.1

Multiply $2$ by $3$ .

$7 x^{\frac{- 2 + 6}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 10.6.2

Add $- 2$ and $6$ .

$7 x^{\frac{4}{3}} + \frac{- 5 x}{x^{\frac{2}{3}}} + \frac{9}{x^{\frac{2}{3}}}$

Step 11

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$7 x^{\frac{4}{3}} - 5 x \cdot x^{- \frac{2}{3}} + \frac{9}{x^{\frac{2}{3}}}$

Step 12

Multiply $x$ by $x^{- \frac{2}{3}}$ by adding the exponents.

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Step 12.1

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

$7 x^{\frac{4}{3}} - 5 (x^{- \frac{2}{3}} x) + \frac{9}{x^{\frac{2}{3}}}$

Step 12.2

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

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Step 12.2.1

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

$7 x^{\frac{4}{3}} - 5 (x^{- \frac{2}{3}} x^{1}) + \frac{9}{x^{\frac{2}{3}}}$

Step 12.2.2

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

$7 x^{\frac{4}{3}} - 5 x^{- \frac{2}{3} + 1} + \frac{9}{x^{\frac{2}{3}}}$

Step 12.3

Write $1$ as a fraction with a common denominator.

$7 x^{\frac{4}{3}} - 5 x^{- \frac{2}{3} + \frac{3}{3}} + \frac{9}{x^{\frac{2}{3}}}$

Step 12.4

Combine the numerators over the common denominator.

$7 x^{\frac{4}{3}} - 5 x^{\frac{- 2 + 3}{3}} + \frac{9}{x^{\frac{2}{3}}}$

Step 12.5

Add $- 2$ and $3$ .

$7 x^{\frac{4}{3}} - 5 x^{\frac{1}{3}} + \frac{9}{x^{\frac{2}{3}}}$