Linear Algebra Examples

$\frac{9 x - 36}{7 x - 28}$

Step 1

Set the denominator in $\frac{9 x - 36}{7 x - 28}$ equal to $0$ to find where the expression is undefined.

$7 x - 28 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $28$ to both sides of the equation.

$7 x = 28$

Step 2.2

Divide each term in $7 x = 28$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 x = 28$ by $7$ .

$\frac{7 x}{7} = \frac{28}{7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{28}{7}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{7}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $28$ by $7$ .

$x = 4$

Step 3

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

Interval Notation:

$(- \infty, 4) \cup (4, \infty)$

Set-Builder Notation:

${x | x \neq 4}$

Step 4