Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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 $b = n$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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