Questions: 55/(6(3-2)+5)+2(3)^2/(8-2)

55/(6(3-2)+5)+2(3)^2/(8-2)
Transcript text: $\frac{55}{6(3-2)+5}+\frac{2(3)^{2}}{8-2}$
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Solution

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To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, simplify the expressions inside the parentheses, then handle the exponents, followed by any multiplication or division, and finally perform the addition.

Paso 1: Simplificación de la primera fracción

Calculamos el denominador de la primera fracción: \[ 6(3 - 2) + 5 = 6(1) + 5 = 6 + 5 = 11 \] Por lo tanto, la primera fracción es: \[ \frac{55}{11} = 5.0 \]

Paso 2: Simplificación de la segunda fracción

Calculamos el numerador y el denominador de la segunda fracción: \[ 2(3^2) = 2(9) = 18 \] \[ 8 - 2 = 6 \] Así que la segunda fracción es: \[ \frac{18}{6} = 3.0 \]

Paso 3: Suma de las fracciones

Sumamos las dos fracciones obtenidas: \[ 5.0 + 3.0 = 8.0 \]

Respuesta Final

\(\boxed{8.0}\)

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