Evaluate the Function g(3)=(x^2+8)/(x^3-25x)

$g (3) = \frac{x^{2} + 8}{x^{3} - 25 x}$

Step 1

Replace the variable $x$ with $3$ in the expression.

$g (3) = \frac{{(3)}^{2} + 8}{{(3)}^{3} - 25 \cdot 3}$

Step 2

Simplify the result.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$g (3) = \frac{9 + 8}{3^{3} - 25 \cdot 3}$

Add $9$ and $8$ .

$g (3) = \frac{17}{3^{3} - 25 \cdot 3}$

Simplify the denominator.

Raise $3$ to the power of $3$ .

$g (3) = \frac{17}{27 - 25 \cdot 3}$

Multiply $- 25$ by $3$ .

$g (3) = \frac{17}{27 - 75}$

Subtract $75$ from $27$ .

$g (3) = \frac{17}{- 48}$

Move the negative in front of the fraction.

$g (3) = - \frac{17}{48}$

The final answer is $- \frac{17}{48}$ .

$- \frac{17}{48}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{17}{48}$

Decimal Form:

$- 0.3541\overline{6}$

Step 4