Precalculus Examples

$(10 m - 15 n) \div \frac{{(2 m - 3 n)}^{2}}{2 m}$

Step 1

Set the denominator in $\frac{{(2 m - 3 n)}^{2}}{2 m}$ equal to $0$ to find where the expression is undefined.

$2 m = 0$

Step 2

Divide each term in $2 m = 0$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 m = 0$ by $2$ .

$\frac{2 m}{2} = \frac{0}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{0}{2}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{0}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $2$ .

$m = 0$

Step 3

Set the denominator in $(10 m - 15 n) \div \frac{{(2 m - 3 n)}^{2}}{2 m}$ equal to $0$ to find where the expression is undefined.

$\frac{{(2 m - 3 n)}^{2}}{2 m} = 0$

Step 4

Solve for $m$ .

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Step 4.1

Set the numerator equal to zero.

${(2 m - 3 n)}^{2} = 0$

Step 4.2

Solve the equation for $m$ .

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Step 4.2.1

Set the $2 m - 3 n$ equal to $0$ .

$2 m - 3 n = 0$

Step 4.2.2

Solve for $m$ .

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Step 4.2.2.1

Add $3 n$ to both sides of the equation.

$2 m = 3 n$

Step 4.2.2.2

Divide each term in $2 m = 3 n$ by $2$ and simplify.

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Step 4.2.2.2.1

Divide each term in $2 m = 3 n$ by $2$ .

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

Step 4.2.2.2.2

Simplify the left side.

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Step 4.2.2.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.2.2.1.2

Divide $m$ by $1$ .

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

Step 5

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

Set-Builder Notation:

${m | m \neq 0, m \neq \frac{3 n}{2}}$ , for any integer $n$