Algebra Examples

$\frac{3 m + n}{n - 1} \cdot \frac{n^{2} - n}{5}$

Step 1

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

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Step 1.1

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

$\frac{3 m + n}{n - 1} \cdot \frac{n \cdot n - n}{5}$

Step 1.2

Factor $n$ out of $- n$ .

$\frac{3 m + n}{n - 1} \cdot \frac{n \cdot n + n \cdot - 1}{5}$

Step 1.3

Factor $n$ out of $n \cdot n + n \cdot - 1$ .

$\frac{3 m + n}{n - 1} \cdot \frac{n (n - 1)}{5}$

Step 2

Cancel the common factor of $n - 1$ .

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Step 2.1

Factor $n - 1$ out of $n (n - 1)$ .

$\frac{3 m + n}{n - 1} \cdot \frac{(n - 1) n}{5}$

Step 2.2

Cancel the common factor.

$\frac{3 m + n}{n - 1} \cdot \frac{(n - 1) n}{5}$

Step 2.3

Rewrite the expression.

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $3 m \frac{n}{5}$ .

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Step 4.1

Combine $3$ and $\frac{n}{5}$ .

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

Step 4.2

Combine $m$ and $\frac{3 n}{5}$ .

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

Step 5

Multiply $n \frac{n}{5}$ .

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Step 5.1

Combine $n$ and $\frac{n}{5}$ .

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

Step 5.2

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

$\frac{m (3 n)}{5} + \frac{n^{1} n}{5}$

Step 5.3

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

$\frac{m (3 n)}{5} + \frac{n^{1} n^{1}}{5}$

Step 5.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m (3 n)}{5} + \frac{n^{1 + 1}}{5}$

Step 5.5

Add $1$ and $1$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

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

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Step 8.1

Factor $n$ out of $3 m n$ .

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

Step 8.2

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

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

Step 8.3

Factor $n$ out of $n (3 m) + n \cdot n$ .

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