Algebra Examples

$m (x) = \frac{x + 5}{x - 1}$ $n (x) = x - 3$

Step 1

Set up the composite result function.

$n (m (x))$

Step 2

Evaluate $n (\frac{x + 5}{x - 1})$ by substituting in the value of $m$ into $n$ .

$n (\frac{x + 5}{x - 1}) = (\frac{x + 5}{x - 1}) - 3$

Step 3

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$n (\frac{x + 5}{x - 1}) = \frac{x + 5}{x - 1} - 3 \cdot \frac{x - 1}{x - 1}$

Step 4

Simplify terms.

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Step 4.1

Combine $- 3$ and $\frac{x - 1}{x - 1}$ .

$n (\frac{x + 5}{x - 1}) = \frac{x + 5}{x - 1} + \frac{- 3 (x - 1)}{x - 1}$

Step 4.2

Combine the numerators over the common denominator.

$n (\frac{x + 5}{x - 1}) = \frac{x + 5 - 3 (x - 1)}{x - 1}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$n (\frac{x + 5}{x - 1}) = \frac{x + 5 - 3 x - 3 \cdot - 1}{x - 1}$

Step 5.2

Multiply $- 3$ by $- 1$ .

$n (\frac{x + 5}{x - 1}) = \frac{x + 5 - 3 x + 3}{x - 1}$

Step 5.3

Subtract $3 x$ from $x$ .

$n (\frac{x + 5}{x - 1}) = \frac{- 2 x + 5 + 3}{x - 1}$

Step 5.4

Add $5$ and $3$ .

$n (\frac{x + 5}{x - 1}) = \frac{- 2 x + 8}{x - 1}$

Step 5.5

Factor $2$ out of $- 2 x + 8$ .

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Step 5.5.1

Factor $2$ out of $- 2 x$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- x) + 8}{x - 1}$

Step 5.5.2

Factor $2$ out of $8$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- x) + 2 (4)}{x - 1}$

Step 5.5.3

Factor $2$ out of $2 (- x) + 2 (4)$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- x + 4)}{x - 1}$

Step 6

Simplify with factoring out.

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Step 6.1

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

$n (\frac{x + 5}{x - 1}) = \frac{2 (- (x) + 4)}{x - 1}$

Step 6.2

Rewrite $4$ as $- 1 (- 4)$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- (x) - 1 \cdot - 4)}{x - 1}$

Step 6.3

Factor $- 1$ out of $- (x) - 1 (- 4)$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- (x - 4))}{x - 1}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (x - 4)$ as $- 1 (x - 4)$ .

$n (\frac{x + 5}{x - 1}) = \frac{2 (- 1 (x - 4))}{x - 1}$

Step 6.4.2

Move the negative in front of the fraction.

$n (\frac{x + 5}{x - 1}) = - \frac{2 (x - 4)}{x - 1}$