Algebra Examples

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

Step 1

Cancel the common factor of $3 m^{2} - 3 n^{2}$ and $6 m - 6 n$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $6 m$ .

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

Step 1.4.2

Factor $3$ out of $- 6 n$ .

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

Step 1.4.3

Factor $3$ out of $3 (2 m) + 3 (- 2 n)$ .

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

Step 1.4.4

Cancel the common factor.

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

Step 1.4.5

Rewrite the expression.

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = n$ .

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

Step 3

Simplify terms.

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Step 3.1

Factor $2$ out of $2 m - 2 n$ .

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Step 3.1.1

Factor $2$ out of $2 m$ .

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

Step 3.1.2

Factor $2$ out of $- 2 n$ .

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

Step 3.1.3

Factor $2$ out of $2 (m) + 2 (- n)$ .

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

Step 3.2

Cancel the common factor of $m - n$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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