Precalculus Examples

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

Step 1

Set the denominator in $\frac{m - n}{m n}$ equal to $0$ to find where the expression is undefined.

$m n = 0$

Step 2

Divide each term in $m n = 0$ by $n$ and simplify.

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Step 2.1

Divide each term in $m n = 0$ by $n$ .

$\frac{m n}{n} = \frac{0}{n}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $n$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{m n}{n} = \frac{0}{n}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{0}{n}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $n$ .

$m = 0$

Step 3

Set the denominator in $\frac{2 m n}{m n - m^{2}}$ equal to $0$ to find where the expression is undefined.

$m n - m^{2} = 0$

Step 4

The domain is all values of $m$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${m | m \neq 0}$