Finite Math Examples

$\frac{s^{2} + 6 s}{s^{2} + 10 s + 24} \cdot \frac{s - 4}{s + 4}$

Step 1

Set the denominator in $\frac{s^{2} + 6 s}{s^{2} + 10 s + 24}$ equal to $0$ to find where the expression is undefined.

$s^{2} + 10 s + 24 = 0$

Step 2

Solve for $s$ .

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Step 2.1

Factor $s^{2} + 10 s + 24$ using the AC method.

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Step 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 $24$ and whose sum is $10$ .

$4, 6$

Step 2.1.2

Write the factored form using these integers.

$(s + 4) (s + 6) = 0$

Step 2.2

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

$s + 4 = 0$

$s + 6 = 0$

Step 2.3

Set $s + 4$ equal to $0$ and solve for $s$ .

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Step 2.3.1

Set $s + 4$ equal to $0$ .

$s + 4 = 0$

Step 2.3.2

Subtract $4$ from both sides of the equation.

$s = - 4$

Step 2.4

Set $s + 6$ equal to $0$ and solve for $s$ .

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Step 2.4.1

Set $s + 6$ equal to $0$ .

$s + 6 = 0$

Step 2.4.2

Subtract $6$ from both sides of the equation.

$s = - 6$

Step 2.5

The final solution is all the values that make $(s + 4) (s + 6) = 0$ true.

$s = - 4, - 6$

Step 3

Set the denominator in $\frac{s - 4}{s + 4}$ equal to $0$ to find where the expression is undefined.

$s + 4 = 0$

Step 4

Subtract $4$ from both sides of the equation.

$s = - 4$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$s = - 6, s = - 4$

Step 6