Pregunta
\( 1 \leftarrow \quad \begin{array}{l}\frac{x^{2}+6}{x^{2}-6 x+8} \\ \frac{x^{2}+6}{x^{2}-6 x+8} \\ \text { (Simplify your answer.) }\end{array} \)
Ask by Guzman Higgins. in Colombia
Feb 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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La expresión simplificada es \(1+\frac{6x-2}{x^{2}-6x+8}\).
Solución
Calculate or simplify the expression \( (x^2+6)/(x^2-6x+8) \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{\left(x^{2}+6\right)}{\left(x^{2}-6x+8\right)}\)
- step1: Calculate:
\(1+\frac{6x-2}{x^{2}-6x+8}\)
La expresión simplificada es \(1+\frac{6x-2}{x^{2}-6x+8}\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To simplify the expression \(\frac{x^{2}+6}{x^{2}-6 x+8}\), we first need to factor the denominator. The expression \(x^{2}-6x+8\) can be factored as \((x-2)(x-4)\). Now the expression becomes: \[ \frac{x^{2}+6}{(x-2)(x-4)} \] Since \(x^{2}+6\) does not factor further and does not share any common factors with \((x-2)(x-4)\), we cannot simplify the fraction any further. Thus, the simplified expression remains: \[ \frac{x^{2}+6}{(x-2)(x-4)} \] Just be careful when substituting values for \(x\); \(x\) cannot be 2 or 4 as these will make the denominator zero!
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