To simplify the expression given, let's rewrite and evaluate it step by step:
-
Expression Provided: \(3x + 184x + \frac{8}{x^2 - 36x + 2}\)
-
Combine Like Terms: \[ 3x + 184x = 187x \] So, the expression becomes: \[ 187x + \frac{8}{x^2 - 36x + 2} \]
-
Factor the Quadratic (if possible): We need to factor \(x^2 - 36x + 2\). Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{36 \pm \sqrt{(-36)^2 - 4 \cdot 1 \cdot 2}}{2 \cdot 1} = \frac{36 \pm \sqrt{1296 - 8}}{2} \] \[ = \frac{36 \pm \sqrt{1288}}{2} = \frac{36 \pm 2\sqrt{322}}{2} = 18 \pm \sqrt{322} \] The quadratic simplifies to \(x^2 - 36x + 2\) and cannot be factored easily.
-
Combine Over a Common Denominator: Rewrite \(187x\) with a common denominator of \(x^2 - 36x + 2\): \[ \frac{187x(x^2 - 36x + 2) + 8}{x^2 - 36x + 2} \]
-
Final Expression Inferring: Since the calculation for the combining of like terms can lead to a more complex expression in the factoring process or finding conditions for \(x\), let's evaluate the simpler choices given:
The answer choices appear to not directly involve the complicated expression of \(x^2 - 36x + 2\).
Let's evaluate the provided answers, assuming simple values where:
- \(x = 6 \Rightarrow 34x - 24 \text{ becomes } 34(6) - 24 = 204 - 24 = 180\).
- None other really simplify in any manner.
The correct expression must come from simplifying or modifying conditions, leading to:
Among the provided choices, without a specific value for \(x\) leading to further calculations, the potentially straightforward one would be in the context of a straightforward function leading directly to \(34x - 8\).
Thus, the simplest form from the choices presented appears to be \(34x - 8\).
So the calculated most suitable one is: \[ \boxed{34x - 8} \]
1 answer