5. STAY (X + 5)/((X - 12)(X - 2)) = 0

A Hidden Message was encrypted and can only be deciphered by answering some rational equations. Each answer corresponds to one word. The arrangement of the words will be given. Your task is to decode the message. Show your solution.


solve this 

We are given the rational equation:

\[
\frac{X + 5}{(X - 12)(X - 2)} = 0
\]

### Step-by-step solution:

1. **Numerator Analysis**: For a rational equation to be equal to 0, the numerator must be 0. The denominator can never be 0, because dividing by 0 is undefined. So, we need to set the numerator equal to 0:

\[
X + 5 = 0
\]

2. **Solve for X**:
   \[
   X = -5
   \]

### Denominator Check:
The denominator is \((X - 12)(X - 2)\), and we must ensure that this does not cause the expression to be undefined. Therefore, we need to find the values of \(X\) that would make the denominator 0.

- \(X - 12 = 0 \implies X = 12\)
- \(X - 2 = 0 \implies X = 2\)

So, \(X\) cannot be \(12\) or \(2\), but \(X = -5\) does not fall into these values. Hence, the solution \(X = -5\) is valid.

### Final Answer:
The solution to the equation is \(X = -5\).

Let me know if you need further details on the decoding process, or if you have any questions!

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Here are 5 related questions for practice:
1. Solve \(\frac{X + 3}{(X - 7)(X + 1)} = 0\).
2. What are the excluded values for \(\frac{X^2 - 9}{X^2 - 16} = 0\)?
3. Solve \(\frac{2X - 4}{(X + 8)(X - 5)} = 0\).
4. How do you find the domain of a rational function?
5. Solve the equation \(\frac{X^2 - 4X}{X^2 - 4} = 0\).

**Tip**: When solving rational equations, always check the denominator to avoid undefined values in your solution.

5. STAY (X + 5)/((X - 12)(X - 2)) = 0
A Hidden Message was encrypted and can only be deciphered by answering some rational equations. Each answer corresponds to one word. The arrangement of the words will be given. Your task is to decode the message. Show your solution.

Learn how to solve the rational equation (X + 5)/((X - 12)(X - 2)) = 0. This step-by-step solution explains key algebraic concepts such as numerator and denominator rules, and applying the zero-product property. Suitable for Grades 9-11.

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