Find the Domain of the Quotient of the Two Functions f(x)=(x-1)/(2x) , g(x)=(x-1)/x

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

Find the quotient of the functions.

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

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

Simplify.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{1}{x \cdot 2} x$

Cancel the common factor.

$\frac{1}{x \cdot 2} x$

Rewrite the expression.

$\frac{1}{2}$

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Find the Domain of the Quotient of the Two Functions f(x)=(x-1)/(2x) , g(x)=(x-1)/x

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