Precalculus Examples

$x y = 1$

Step 1

Divide each term in $x y = 1$ by $x$ and simplify.

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Step 1.1

Divide each term in $x y = 1$ by $x$ .

$\frac{x y}{x} = \frac{1}{x}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $x$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{x y}{x} = \frac{1}{x}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{x}$

Step 2

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{1}{x}$