Precalculus Examples

$f (x) = \frac{x + 3}{x + 1}$ , $\frac{f (x) - f (1)}{x - 1}$

Step 1

Evaluate the numerator in $\frac{f (x) - f \cdot 1}{x - 1}$ .

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Step 1.1

Replace the function designators in $f (x) - f \cdot 1$ with the actual functions.

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

Step 1.2

Simplify $(\frac{x + 3}{x + 1}) - \frac{x + 3}{x + 1} \cdot 1$ .

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Step 1.2.1

Multiply $- 1$ by $1$ .

$\frac{x + 3}{x + 1} - \frac{x + 3}{x + 1}$

Step 1.2.2

Subtract $\frac{x + 3}{x + 1}$ from $\frac{x + 3}{x + 1}$ .

$0$

Step 2

Rewrite $\frac{f (x) - f \cdot 1}{x - 1}$ .

$\frac{0}{x - 1}$

Step 3

Divide $0$ by $x - 1$ .

$0$