Basic Math Examples

$\frac{30 n^{2}}{15 n} + \frac{40 n^{4}}{10 n^{3}}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $30$ and $15$ .

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Step 1.1.1

Factor $15$ out of $30 n^{2}$ .

$\frac{15 (2 n^{2})}{15 n} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $15$ out of $15 n$ .

$\frac{15 (2 n^{2})}{15 (n)} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.1.2.2

Cancel the common factor.

$\frac{15 (2 n^{2})}{15 n} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.1.2.3

Rewrite the expression.

$\frac{2 n^{2}}{n} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2

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

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Step 1.2.1

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

$\frac{n (2 n)}{n} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

$\frac{n (2 n)}{n^{1}} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2.2.2

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

$\frac{n (2 n)}{n \cdot 1} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2.2.3

Cancel the common factor.

$\frac{n (2 n)}{n \cdot 1} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2.2.4

Rewrite the expression.

$\frac{2 n}{1} + \frac{40 n^{4}}{10 n^{3}}$

Step 1.2.2.5

Divide $2 n$ by $1$ .

$2 n + \frac{40 n^{4}}{10 n^{3}}$

Step 1.3

Cancel the common factor of $40$ and $10$ .

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Step 1.3.1

Factor $10$ out of $40 n^{4}$ .

$2 n + \frac{10 (4 n^{4})}{10 n^{3}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $10$ out of $10 n^{3}$ .

$2 n + \frac{10 (4 n^{4})}{10 (n^{3})}$

Step 1.3.2.2

Cancel the common factor.

$2 n + \frac{10 (4 n^{4})}{10 n^{3}}$

Step 1.3.2.3

Rewrite the expression.

$2 n + \frac{4 n^{4}}{n^{3}}$

Step 1.4

Cancel the common factor of $n^{4}$ and $n^{3}$ .

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Step 1.4.1

Factor $n^{3}$ out of $4 n^{4}$ .

$2 n + \frac{n^{3} (4 n)}{n^{3}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Multiply by $1$ .

$2 n + \frac{n^{3} (4 n)}{n^{3} \cdot 1}$

Step 1.4.2.2

Cancel the common factor.

$2 n + \frac{n^{3} (4 n)}{n^{3} \cdot 1}$

Step 1.4.2.3

Rewrite the expression.

$2 n + \frac{4 n}{1}$

Step 1.4.2.4

Divide $4 n$ by $1$ .

$2 n + 4 n$

Step 2

Add $2 n$ and $4 n$ .

$6 n$