Pre-Algebra Examples

$\frac{9 x m n^{2} + 6 x m^{2} n + 45 x^{2} m n}{9 x m^{2} n}$

Step 1

Factor $3 x m n$ out of $9 x m n^{2} + 6 x m^{2} n + 45 x^{2} m n$ .

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Step 1.1

Factor $3 x m n$ out of $9 x m n^{2}$ .

$\frac{3 x m n (3 n) + 6 x m^{2} n + 45 x^{2} m n}{9 x m^{2} n}$

Step 1.2

Factor $3 x m n$ out of $6 x m^{2} n$ .

$\frac{3 x m n (3 n) + 3 x m n (2 m) + 45 x^{2} m n}{9 x m^{2} n}$

Step 1.3

Factor $3 x m n$ out of $45 x^{2} m n$ .

$\frac{3 x m n (3 n) + 3 x m n (2 m) + 3 x m n (15 x)}{9 x m^{2} n}$

Step 1.4

Factor $3 x m n$ out of $3 x m n (3 n) + 3 x m n (2 m)$ .

$\frac{3 x m n (3 n + 2 m) + 3 x m n (15 x)}{9 x m^{2} n}$

Step 1.5

Factor $3 x m n$ out of $3 x m n (3 n + 2 m) + 3 x m n (15 x)$ .

$\frac{3 x m n (3 n + 2 m + 15 x)}{9 x m^{2} n}$

Step 2

Cancel the common factor of $3$ and $9$ .

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Step 2.1

Factor $3$ out of $3 x m n (3 n + 2 m + 15 x)$ .

$\frac{3 (x m n (3 n + 2 m + 15 x))}{9 x m^{2} n}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $9 x m^{2} n$ .

$\frac{3 (x m n (3 n + 2 m + 15 x))}{3 (3 x m^{2} n)}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (x m n (3 n + 2 m + 15 x))}{3 (3 x m^{2} n)}$

Step 2.2.3

Rewrite the expression.

$\frac{x m n (3 n + 2 m + 15 x)}{3 x m^{2} n}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x m n (3 n + 2 m + 15 x)}{3 x m^{2} n}$

Step 3.2

Rewrite the expression.

$\frac{m n (3 n + 2 m + 15 x)}{3 m^{2} n}$

Step 4

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

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Step 4.1

Factor $m$ out of $m n (3 n + 2 m + 15 x)$ .

$\frac{m (n (3 n + 2 m + 15 x))}{3 m^{2} n}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m$ out of $3 m^{2} n$ .

$\frac{m (n (3 n + 2 m + 15 x))}{m (3 m n)}$

Step 4.2.2

Cancel the common factor.

$\frac{m (n (3 n + 2 m + 15 x))}{m (3 m n)}$

Step 4.2.3

Rewrite the expression.

$\frac{n (3 n + 2 m + 15 x)}{3 m n}$

Step 5

Cancel the common factor of $n$ .

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Step 5.1

Cancel the common factor.

$\frac{n (3 n + 2 m + 15 x)}{3 m n}$

Step 5.2

Rewrite the expression.

$\frac{3 n + 2 m + 15 x}{3 m}$

Step 6

Split the fraction $\frac{3 n + 2 m + 15 x}{3 m}$ into two fractions.

$\frac{3 n + 2 m}{3 m} + \frac{15 x}{3 m}$

Step 7

Split the fraction $\frac{3 n + 2 m}{3 m}$ into two fractions.

$\frac{3 n}{3 m} + \frac{2 m}{3 m} + \frac{15 x}{3 m}$

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Cancel the common factor.

$\frac{3 n}{3 m} + \frac{2 m}{3 m} + \frac{15 x}{3 m}$

Step 8.2

Rewrite the expression.

$\frac{n}{m} + \frac{2 m}{3 m} + \frac{15 x}{3 m}$

Step 9

Cancel the common factor of $m$ .

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Step 9.1

Cancel the common factor.

$\frac{n}{m} + \frac{2 m}{3 m} + \frac{15 x}{3 m}$

Step 9.2

Rewrite the expression.

$\frac{n}{m} + \frac{2}{3} + \frac{15 x}{3 m}$

Step 10

Cancel the common factor of $15$ and $3$ .

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Step 10.1

Factor $3$ out of $15 x$ .

$\frac{n}{m} + \frac{2}{3} + \frac{3 (5 x)}{3 m}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3 m$ .

$\frac{n}{m} + \frac{2}{3} + \frac{3 (5 x)}{3 (m)}$

Step 10.2.2

Cancel the common factor.

$\frac{n}{m} + \frac{2}{3} + \frac{3 (5 x)}{3 m}$

Step 10.2.3

Rewrite the expression.

$\frac{n}{m} + \frac{2}{3} + \frac{5 x}{m}$