Find the Intersection of the Functions f(x)=1/(x-2) , f(x)=1

$f (x) = \frac{1}{(x - 2)}$ , $f (x) = 1$

Substitute $1$ for $f (x)$ .

$1 = \frac{1}{x - 2}$

Solve for $x$ .

Rewrite the equation as $\frac{1}{x - 2} = 1$ .

$\frac{1}{x - 2} = 1$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 2, 1$

Remove parentheses.

$x - 2, 1$

The LCM of one and any expression is the expression.

$x - 2$

Multiply each term in $\frac{1}{x - 2} = 1$ by $x - 2$ to eliminate the fractions.

Multiply each term in $\frac{1}{x - 2} = 1$ by $x - 2$ .

$\frac{1}{x - 2} (x - 2) = 1 (x - 2)$

Simplify the left side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{1}{x - 2} (x - 2) = 1 (x - 2)$

Rewrite the expression.

$1 = 1 (x - 2)$

Simplify the right side.

Multiply $x - 2$ by $1$ .

$1 = x - 2$

Solve the equation.

Rewrite the equation as $x - 2 = 1$ .

$x - 2 = 1$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 1 + 2$

Add $1$ and $2$ .

$x = 3$