Algebra Examples

$f (x) = - 3 x - 1$ , $h (x) = - \frac{15}{x - 4}$

Step 1

Set up the composite result function.

$f (h (x))$

Step 2

Evaluate $f (- \frac{15}{x - 4})$ by substituting in the value of $h$ into $f$ .

$f (- \frac{15}{x - 4}) = - 3 (- \frac{15}{x - 4}) - 1$

Step 3

Multiply $- 3 (- \frac{15}{x - 4})$ .

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Step 3.1

Multiply $- 1$ by $- 3$ .

$f (- \frac{15}{x - 4}) = 3 (\frac{15}{x - 4}) - 1$

Step 3.2

Combine $3$ and $\frac{15}{x - 4}$ .

$f (- \frac{15}{x - 4}) = \frac{3 \cdot 15}{x - 4} - 1$

Step 3.3

Multiply $3$ by $15$ .

$f (- \frac{15}{x - 4}) = \frac{45}{x - 4} - 1$

Step 4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$f (- \frac{15}{x - 4}) = \frac{45}{x - 4} - 1 \cdot \frac{x - 4}{x - 4}$

Step 5

Simplify terms.

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Step 5.1

Combine $- 1$ and $\frac{x - 4}{x - 4}$ .

$f (- \frac{15}{x - 4}) = \frac{45}{x - 4} + \frac{- (x - 4)}{x - 4}$

Step 5.2

Combine the numerators over the common denominator.

$f (- \frac{15}{x - 4}) = \frac{45 - (x - 4)}{x - 4}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$f (- \frac{15}{x - 4}) = \frac{45 - x + 4}{x - 4}$

Step 6.2

Multiply $- 1$ by $- 4$ .

$f (- \frac{15}{x - 4}) = \frac{45 - x + 4}{x - 4}$

Step 6.3

Add $45$ and $4$ .

$f (- \frac{15}{x - 4}) = \frac{- x + 49}{x - 4}$

Step 7

Simplify with factoring out.

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Step 7.1

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

$f (- \frac{15}{x - 4}) = \frac{- (x) + 49}{x - 4}$

Step 7.2

Rewrite $49$ as $- 1 (- 49)$ .

$f (- \frac{15}{x - 4}) = \frac{- (x) - 1 \cdot - 49}{x - 4}$

Step 7.3

Factor $- 1$ out of $- (x) - 1 (- 49)$ .

$f (- \frac{15}{x - 4}) = \frac{- (x - 49)}{x - 4}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (x - 49)$ as $- 1 (x - 49)$ .

$f (- \frac{15}{x - 4}) = \frac{- 1 (x - 49)}{x - 4}$

Step 7.4.2

Move the negative in front of the fraction.

$f (- \frac{15}{x - 4}) = - \frac{x - 49}{x - 4}$