Problem

The function $h$ is defined as follows. \[ h(x)=\frac{x^{2}+x-12}{x^{2}-4 x-12} \] Find $h(5)$. Simplify your answer as much as possible. If applicable, click on "Undefined".

Solution

Step 1 :The function h(x) is a rational function, which means it's a ratio of two polynomials. To find h(5), we need to substitute x = 5 into the function and simplify the result.

Step 2 :Substitute x = 5 into the function: \[h(5)=\frac{5^{2}+5-12}{5^{2}-4 \times 5-12}\]

Step 3 :Simplify the result to get a decimal number: h(5) = -2.5714285714285716

Step 4 :Convert the decimal to a fraction to simplify the answer as much as possible: \[h(5) = -\frac{18}{7}\]

Step 5 :Final Answer: \[h(5) = \boxed{-\frac{18}{7}}\]

From Solvely APP
Source: https://solvelyapp.com/problems/16714/

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