Algebra Examples

$g (x) = \frac{x + 6}{x - 1}$ , $h (x) = 2 x + 7$ ,

Step 1

Set up the composite result function.

$h (g (x))$

Step 2

Evaluate $h (\frac{x + 6}{x - 1})$ by substituting in the value of $g$ into $h$ .

$h (\frac{x + 6}{x - 1}) = 2 (\frac{x + 6}{x - 1}) + 7$

Step 3

Combine $2$ and $\frac{x + 6}{x - 1}$ .

$h (\frac{x + 6}{x - 1}) = \frac{2 (x + 6)}{x - 1} + 7$

Step 4

To write $7$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$h (\frac{x + 6}{x - 1}) = \frac{2 (x + 6)}{x - 1} + \frac{7 (x - 1)}{x - 1}$

Step 5

Combine the numerators over the common denominator.

$h (\frac{x + 6}{x - 1}) = \frac{2 (x + 6) + 7 (x - 1)}{x - 1}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$h (\frac{x + 6}{x - 1}) = \frac{2 x + 2 \cdot 6 + 7 (x - 1)}{x - 1}$

Step 6.2

Multiply $2$ by $6$ .

$h (\frac{x + 6}{x - 1}) = \frac{2 x + 12 + 7 (x - 1)}{x - 1}$

Step 6.3

Apply the distributive property.

$h (\frac{x + 6}{x - 1}) = \frac{2 x + 12 + 7 x + 7 \cdot - 1}{x - 1}$

Step 6.4

Multiply $7$ by $- 1$ .

$h (\frac{x + 6}{x - 1}) = \frac{2 x + 12 + 7 x - 7}{x - 1}$

Step 6.5

Add $2 x$ and $7 x$ .

$h (\frac{x + 6}{x - 1}) = \frac{9 x + 12 - 7}{x - 1}$

Step 6.6

Subtract $7$ from $12$ .

$h (\frac{x + 6}{x - 1}) = \frac{9 x + 5}{x - 1}$