Finite Math Examples

$f (x) = \frac{x^{2} - 13 x + 36}{x^{2} - 64}$

Step 1

Set $\frac{x^{2} - 13 x + 36}{x^{2} - 64}$ equal to $0$ .

$\frac{x^{2} - 13 x + 36}{x^{2} - 64} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$x^{2} - 13 x + 36 = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Factor $x^{2} - 13 x + 36$ using the AC method.

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Step 2.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $36$ and whose sum is $- 13$ .

$- 9, - 4$

Step 2.2.1.2

Write the factored form using these integers.

$(x - 9) (x - 4) = 0$

Step 2.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 9 = 0$

$x - 4 = 0$

Step 2.2.3

Set $x - 9$ equal to $0$ and solve for $x$ .

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Step 2.2.3.1

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Step 2.2.3.2

Add $9$ to both sides of the equation.

$x = 9$

Step 2.2.4

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.2.4.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.2.4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.2.5

The final solution is all the values that make $(x - 9) (x - 4) = 0$ true.

$x = 9, 4$

Step 3