Pre-Algebra Examples

$\frac{90 x m n^{2} + 12 x m^{2} n + 72 x^{2} m n}{18 x m^{2} n}$

Step 1

Factor $6 x m n$ out of $90 x m n^{2} + 12 x m^{2} n + 72 x^{2} m n$ .

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Step 1.1

Factor $6 x m n$ out of $90 x m n^{2}$ .

$\frac{6 x m n (15 n) + 12 x m^{2} n + 72 x^{2} m n}{18 x m^{2} n}$

Step 1.2

Factor $6 x m n$ out of $12 x m^{2} n$ .

$\frac{6 x m n (15 n) + 6 x m n (2 m) + 72 x^{2} m n}{18 x m^{2} n}$

Step 1.3

Factor $6 x m n$ out of $72 x^{2} m n$ .

$\frac{6 x m n (15 n) + 6 x m n (2 m) + 6 x m n (12 x)}{18 x m^{2} n}$

Step 1.4

Factor $6 x m n$ out of $6 x m n (15 n) + 6 x m n (2 m)$ .

$\frac{6 x m n (15 n + 2 m) + 6 x m n (12 x)}{18 x m^{2} n}$

Step 1.5

Factor $6 x m n$ out of $6 x m n (15 n + 2 m) + 6 x m n (12 x)$ .

$\frac{6 x m n (15 n + 2 m + 12 x)}{18 x m^{2} n}$

Step 2

Cancel the common factor of $6$ and $18$ .

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Step 2.1

Factor $6$ out of $6 x m n (15 n + 2 m + 12 x)$ .

$\frac{6 (x m n (15 n + 2 m + 12 x))}{18 x m^{2} n}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $18 x m^{2} n$ .

$\frac{6 (x m n (15 n + 2 m + 12 x))}{6 (3 x m^{2} n)}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (x m n (15 n + 2 m + 12 x))}{6 (3 x m^{2} n)}$

Step 2.2.3

Rewrite the expression.

$\frac{x m n (15 n + 2 m + 12 x)}{3 x m^{2} n}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x m n (15 n + 2 m + 12 x)}{3 x m^{2} n}$

Step 3.2

Rewrite the expression.

$\frac{m n (15 n + 2 m + 12 x)}{3 m^{2} n}$

Step 4

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

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Step 4.1

Factor $m$ out of $m n (15 n + 2 m + 12 x)$ .

$\frac{m (n (15 n + 2 m + 12 x))}{3 m^{2} n}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{m (n (15 n + 2 m + 12 x))}{m (3 m n)}$

Step 4.2.2

Cancel the common factor.

$\frac{m (n (15 n + 2 m + 12 x))}{m (3 m n)}$

Step 4.2.3

Rewrite the expression.

$\frac{n (15 n + 2 m + 12 x)}{3 m n}$

Step 5

Cancel the common factor of $n$ .

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Step 5.1

Cancel the common factor.

$\frac{n (15 n + 2 m + 12 x)}{3 m n}$

Step 5.2

Rewrite the expression.

$\frac{15 n + 2 m + 12 x}{3 m}$

Step 6

Split the fraction $\frac{15 n + 2 m + 12 x}{3 m}$ into two fractions.

$\frac{15 n + 2 m}{3 m} + \frac{12 x}{3 m}$

Step 7

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

$\frac{15 n}{3 m} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 8

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

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Step 8.1

Factor $3$ out of $15 n$ .

$\frac{3 (5 n)}{3 m} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $3 m$ .

$\frac{3 (5 n)}{3 (m)} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 8.2.2

Cancel the common factor.

$\frac{3 (5 n)}{3 m} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 8.2.3

Rewrite the expression.

$\frac{5 n}{m} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 9

Cancel the common factor of $m$ .

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Step 9.1

Cancel the common factor.

$\frac{5 n}{m} + \frac{2 m}{3 m} + \frac{12 x}{3 m}$

Step 9.2

Rewrite the expression.

$\frac{5 n}{m} + \frac{2}{3} + \frac{12 x}{3 m}$

Step 10

Cancel the common factor of $12$ and $3$ .

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Step 10.1

Factor $3$ out of $12 x$ .

$\frac{5 n}{m} + \frac{2}{3} + \frac{3 (4 x)}{3 m}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3 m$ .

$\frac{5 n}{m} + \frac{2}{3} + \frac{3 (4 x)}{3 (m)}$

Step 10.2.2

Cancel the common factor.

$\frac{5 n}{m} + \frac{2}{3} + \frac{3 (4 x)}{3 m}$

Step 10.2.3

Rewrite the expression.

$\frac{5 n}{m} + \frac{2}{3} + \frac{4 x}{m}$