Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (\frac{1}{x + 1}) = \frac{1 - (\frac{1}{x + 1})}{\frac{1}{x + 1}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{1}{x + 1}) = (1 - \frac{1}{x + 1}) (x + 1)$

Step 4

Combine into one fraction.

Tap for more steps...

Step 4.1

Write $1$ as a fraction with a common denominator.

$g (\frac{1}{x + 1}) = (\frac{x + 1}{x + 1} - \frac{1}{x + 1}) (x + 1)$

Step 4.2

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Subtract $1$ from $1$ .

$g (\frac{1}{x + 1}) = \frac{x + 0}{x + 1} \cdot (x + 1)$

Step 5.2

Add $x$ and $0$ .

$g (\frac{1}{x + 1}) = \frac{x}{x + 1} \cdot (x + 1)$

Step 6

Cancel the common factor of $x + 1$ .

Tap for more steps...

Step 6.1

Cancel the common factor.

$g (\frac{1}{x + 1}) = \frac{x}{x + 1} \cdot (x + 1)$

Step 6.2

Rewrite the expression.

$g (\frac{1}{x + 1}) = x$