Finite Math Examples

$f (x) = \frac{7 x}{x - 8}$ , $g (x) = \frac{6}{8 - x}$

Step 1

Find the sum of the functions.

Tap for more steps...

Step 1.1

Replace the function designators with the actual functions in $f (x) + g (x)$ .

$\frac{7 x}{x - 8} + \frac{6}{8 - x}$

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{7 x}{x - 8} + \frac{6}{- 1 (- 8) - x}$

Step 1.2.2

Factor $- 1$ out of $- x$ .

$\frac{7 x}{x - 8} + \frac{6}{- 1 (- 8) - (x)}$

Step 1.2.3

Factor $- 1$ out of $- 1 (- 8) - (x)$ .

$\frac{7 x}{x - 8} + \frac{6}{- 1 (- 8 + x)}$

Step 1.2.4

Simplify the expression.

Tap for more steps...

Step 1.2.4.1

Move a negative from the denominator of $\frac{6}{- 1 (- 8 + x)}$ to the numerator.

$\frac{7 x}{x - 8} + \frac{- 1 \cdot 6}{- 8 + x}$

Step 1.2.4.2

Reorder terms.

$\frac{7 x}{x - 8} + \frac{- 1 \cdot 6}{x - 8}$

Step 1.2.5

Combine the numerators over the common denominator.

$\frac{7 x - 1 \cdot 6}{x - 8}$

Step 1.2.6

Multiply $- 1$ by $6$ .

$\frac{7 x - 6}{x - 8}$

Step 2

Set the denominator in $\frac{7 x - 6}{x - 8}$ equal to $0$ to find where the expression is undefined.

$x - 8 = 0$

Step 3

Add $8$ to both sides of the equation.

$x = 8$

Step 4

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

Interval Notation:

$(- \infty, 8) \cup (8, \infty)$

Set-Builder Notation:

${x | x \neq 8}$

Step 5