Algebra Examples

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

Step 1

Cancel the common factor of $x$ .

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

To find the holes in the graph, look at the denominator factors that were cancelled.

$x$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{1}{x - 2}$ .

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Step 3.1

Set $x$ equal to $0$ .

$x = 0$

Step 3.2

Substitute $0$ for $x$ in $\frac{1}{x - 2}$ and simplify.

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Step 3.2.1

Substitute $0$ for $x$ to find the $y$ coordinate of the hole.

$\frac{1}{0 - 2}$

Step 3.2.2

Simplify.

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Step 3.2.2.1

Subtract $2$ from $0$ .

$\frac{1}{- 2}$

Step 3.2.2.2

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 3.3

The holes in the graph are the points where any of the cancelled factors are equal to $0$ .

$(0, - \frac{1}{2})$

Step 4