Algebra Examples

$y = \frac{(x - 4) (x + 5)}{(x + 5) (x + 5)}$

Step 1

Factor $(x + 5) (x + 5)$ .

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Step 1.1

Raise $x + 5$ to the power of $1$ .

$y = \frac{(x - 4) (x + 5)}{(x + 5) (x + 5)}$

Step 1.2

Raise $x + 5$ to the power of $1$ .

$y = \frac{(x - 4) (x + 5)}{(x + 5) (x + 5)}$

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{(x - 4) (x + 5)}{{(x + 5)}^{1 + 1}}$

Step 1.4

Add $1$ and $1$ .

$y = \frac{(x - 4) (x + 5)}{{(x + 5)}^{2}}$

Step 2

Cancel the common factor of $x + 5$ and ${(x + 5)}^{2}$ .

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Step 2.1

Factor $x + 5$ out of $(x - 4) (x + 5)$ .

$y = \frac{(x + 5) (x - 4)}{{(x + 5)}^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x + 5$ out of ${(x + 5)}^{2}$ .

$y = \frac{(x + 5) (x - 4)}{(x + 5) (x + 5)}$

Step 2.2.2

Cancel the common factor.

$y = \frac{(x + 5) (x - 4)}{(x + 5) (x + 5)}$

Step 2.2.3

Rewrite the expression.

$y = \frac{x - 4}{x + 5}$

Step 3

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Step 4