Basic Math Examples

$\frac{6 m^{2} - 3 m n}{4 m^{2} - n^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3 m$ out of $6 m^{2} - 3 m n$ .

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Step 1.1.1

Factor $3 m$ out of $6 m^{2}$ .

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

Step 1.1.2

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

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

Step 1.1.3

Factor $3 m$ out of $3 m (2 m) + 3 m (- 1 n)$ .

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

Step 1.2

Rewrite $- 1 n$ as $- n$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4 m^{2}$ as ${(2 m)}^{2}$ .

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

Step 2.2

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

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

Step 3

Cancel the common factor of $2 m - n$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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