Algebra Examples

$x y - 5 y = 1$

Step 1

Factor $y$ out of $x y - 5 y$ .

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Step 1.1

Factor $y$ out of $x y$ .

$y x - 5 y = 1$

Step 1.2

Factor $y$ out of $- 5 y$ .

$y x + y \cdot - 5 = 1$

Step 1.3

Factor $y$ out of $y x + y \cdot - 5$ .

$y (x - 5) = 1$

Step 2

Divide each term in $y (x - 5) = 1$ by $x - 5$ and simplify.

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Step 2.1

Divide each term in $y (x - 5) = 1$ by $x - 5$ .

$\frac{y (x - 5)}{x - 5} = \frac{1}{x - 5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x - 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y (x - 5)}{x - 5} = \frac{1}{x - 5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{x - 5}$

Step 3

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.

$f (x) = \frac{1}{x - 5}$