Algebra Examples

$\frac{3 n - m^{2} n + 2 n}{6 m}$

Step 1

Simplify the numerator.

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Step 1.1

Add $3 n$ and $2 n$ .

$\frac{- m^{2} n + 5 n}{6 m}$

Step 1.2

Factor $n$ out of $- m^{2} n + 5 n$ .

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Step 1.2.1

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

$\frac{n (- m^{2}) + 5 n}{6 m}$

Step 1.2.2

Factor $n$ out of $5 n$ .

$\frac{n (- m^{2}) + n \cdot 5}{6 m}$

Step 1.2.3

Factor $n$ out of $n (- m^{2}) + n \cdot 5$ .

$\frac{n (- m^{2} + 5)}{6 m}$

Step 2

Factor $- 1$ out of $- m^{2}$ .

$\frac{n (- (m^{2}) + 5)}{6 m}$

Step 3

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{n (- (m^{2}) - 1 (- 5))}{6 m}$

Step 4

Factor $- 1$ out of $- (m^{2}) - 1 (- 5)$ .

$\frac{n (- (m^{2} - 5))}{6 m}$

Step 5

Rewrite $- (m^{2} - 5)$ as $- 1 (m^{2} - 5)$ .

$\frac{n (- 1 (m^{2} - 5))}{6 m}$

Step 6

Move the negative in front of the fraction.

$- \frac{n (m^{2} - 5)}{6 m}$

Step 7

Apply the distributive property.

$- \frac{n m^{2} + n \cdot - 5}{6 m}$

Step 8

Move $- 5$ to the left of $n$ .

$- \frac{n m^{2} - 5 n}{6 m}$

Step 9

Split the fraction $\frac{n m^{2} - 5 n}{6 m}$ into two fractions.

$- (\frac{n m^{2}}{6 m} + \frac{- 5 n}{6 m})$

Step 10

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

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Step 10.1

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

$- (\frac{m (n m)}{6 m} + \frac{- 5 n}{6 m})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $m$ out of $6 m$ .

$- (\frac{m (n m)}{m \cdot 6} + \frac{- 5 n}{6 m})$

Step 10.2.2

Cancel the common factor.

$- (\frac{m (n m)}{m \cdot 6} + \frac{- 5 n}{6 m})$

Step 10.2.3

Rewrite the expression.

$- (\frac{n m}{6} + \frac{- 5 n}{6 m})$

Step 11

Move the negative in front of the fraction.

$- (\frac{n m}{6} - \frac{5 n}{6 m})$