Algebra Examples

$\frac{m x + m y}{5 n} \cdot \frac{10 m}{n y + n x}$

Step 1

Factor $m$ out of $m x + m y$ .

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Step 1.1

Factor $m$ out of $m x$ .

$\frac{m (x) + m y}{5 n} \cdot \frac{10 m}{n y + n x}$

Step 1.2

Factor $m$ out of $m y$ .

$\frac{m (x) + m (y)}{5 n} \cdot \frac{10 m}{n y + n x}$

Step 1.3

Factor $m$ out of $m (x) + m (y)$ .

$\frac{m (x + y)}{5 n} \cdot \frac{10 m}{n y + n x}$

Step 2

Factor $n$ out of $n y + n x$ .

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Step 2.1

Factor $n$ out of $n y$ .

$\frac{m (x + y)}{5 n} \cdot \frac{10 m}{n (y) + n x}$

Step 2.2

Factor $n$ out of $n x$ .

$\frac{m (x + y)}{5 n} \cdot \frac{10 m}{n (y) + n (x)}$

Step 2.3

Factor $n$ out of $n (y) + n (x)$ .

$\frac{m (x + y)}{5 n} \cdot \frac{10 m}{n (y + x)}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Factor $5$ out of $5 n$ .

$\frac{m (x + y)}{5 (n)} \cdot \frac{10 m}{n (y + x)}$

Step 3.2

Factor $5$ out of $10 m$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$\frac{m (x + y)}{n} \cdot \frac{2 m}{n (y + x)}$

Step 4

Multiply $\frac{m (x + y)}{n}$ by $\frac{2 m}{n (y + x)}$ .

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

Step 5

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

$\frac{m^{1} m (x + y) \cdot 2}{n (n (y + x))}$

Step 6

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

$\frac{m^{1} m^{1} (x + y) \cdot 2}{n (n (y + x))}$

Step 7

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

$\frac{m^{1 + 1} (x + y) \cdot 2}{n (n (y + x))}$

Step 8

Add $1$ and $1$ .

$\frac{m^{2} (x + y) \cdot 2}{n (n (y + x))}$

Step 9

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

$\frac{m^{2} (x + y) \cdot 2}{n^{1} n (y + x)}$

Step 10

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

$\frac{m^{2} (x + y) \cdot 2}{n^{1} n^{1} (y + x)}$

Step 11

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

$\frac{m^{2} (x + y) \cdot 2}{n^{1 + 1} (y + x)}$

Step 12

Add $1$ and $1$ .

$\frac{m^{2} (x + y) \cdot 2}{n^{2} (y + x)}$

Step 13

Cancel the common factor of $x + y$ and $y + x$ .

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Step 13.1

Reorder terms.

$\frac{m^{2} (x + y) \cdot 2}{n^{2} (x + y)}$

Step 13.2

Cancel the common factor.

$\frac{m^{2} (x + y) \cdot 2}{n^{2} (x + y)}$

Step 13.3

Rewrite the expression.

$\frac{m^{2} \cdot 2}{n^{2}}$

Step 14

Move $2$ to the left of $m^{2}$ .

$\frac{2 m^{2}}{n^{2}}$