Linear Algebra Examples

$\frac{6 - 2}{8 + 5 x - 1}$

Step 1

Set the denominator in $\frac{6 - 2}{8 + 5 x - 1}$ equal to $0$ to find where the expression is undefined.

$8 + 5 x - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $1$ from $8$ .

$5 x + 7 = 0$

Step 2.2

Subtract $7$ from both sides of the equation.

$5 x = - 7$

Step 2.3

Divide each term in $5 x = - 7$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = - 7$ by $5$ .

$\frac{5 x}{5} = \frac{- 7}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 7}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

Step 3

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

Interval Notation:

$(- \infty, - \frac{7}{5}) \cup (- \frac{7}{5}, \infty)$

Set-Builder Notation:

${x | x \neq - \frac{7}{5}}$

Step 4