Pre-Algebra Examples

$\frac{21 m^{2} n^{2} - 28 m n^{3} + 21 m^{2} n}{21 m^{2} n}$

Step 1

Factor $7 m n$ out of $21 m^{2} n^{2} - 28 m n^{3} + 21 m^{2} n$ .

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Step 1.1

Factor $7 m n$ out of $21 m^{2} n^{2}$ .

$\frac{7 m n (3 m n) - 28 m n^{3} + 21 m^{2} n}{21 m^{2} n}$

Step 1.2

Factor $7 m n$ out of $- 28 m n^{3}$ .

$\frac{7 m n (3 m n) + 7 m n (- 4 n^{2}) + 21 m^{2} n}{21 m^{2} n}$

Step 1.3

Factor $7 m n$ out of $21 m^{2} n$ .

$\frac{7 m n (3 m n) + 7 m n (- 4 n^{2}) + 7 m n (3 m)}{21 m^{2} n}$

Step 1.4

Factor $7 m n$ out of $7 m n (3 m n) + 7 m n (- 4 n^{2})$ .

$\frac{7 m n (3 m n - 4 n^{2}) + 7 m n (3 m)}{21 m^{2} n}$

Step 1.5

Factor $7 m n$ out of $7 m n (3 m n - 4 n^{2}) + 7 m n (3 m)$ .

$\frac{7 m n (3 m n - 4 n^{2} + 3 m)}{21 m^{2} n}$

Step 2

Cancel the common factor of $7$ and $21$ .

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Step 2.1

Factor $7$ out of $7 m n (3 m n - 4 n^{2} + 3 m)$ .

$\frac{7 (m n (3 m n - 4 n^{2} + 3 m))}{21 m^{2} n}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $7$ out of $21 m^{2} n$ .

$\frac{7 (m n (3 m n - 4 n^{2} + 3 m))}{7 (3 m^{2} n)}$

Step 2.2.2

Cancel the common factor.

$\frac{7 (m n (3 m n - 4 n^{2} + 3 m))}{7 (3 m^{2} n)}$

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Factor $m$ out of $m n (3 m n - 4 n^{2} + 3 m)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $n$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Split the fraction $\frac{3 m n - 4 n^{2} + 3 m}{3 m}$ into two fractions.

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

Step 6

Split the fraction $\frac{3 m n - 4 n^{2}}{3 m}$ into two fractions.

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

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Cancel the common factor of $m$ .

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Step 8.1

Cancel the common factor.

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

Step 8.2

Divide $n$ by $1$ .

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Cancel the common factor.

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

Step 10.2

Rewrite the expression.

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

Step 11

Cancel the common factor of $m$ .

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Step 11.1

Cancel the common factor.

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

Step 11.2

Rewrite the expression.

$n - \frac{4 n^{2}}{3 m} + 1$