Gordon Osborne
05/31/2023 · High School
a) 15 de \( \frac{1}{3}=5 \) b) 24 D \( \frac{2}{6}=8 \) c) \( 32 d t \frac{3}{6}=12 \) d) \( 21 d \in \frac{4}{1}=12 \) RESolve IAS siguiEN \( a=\frac{180}{4 \sqrt{45}}+\frac{30}{45}= \)
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Step-by-step Solution
Para resolver la expresión \( a = \frac{180}{4 \sqrt{45}} + \frac{30}{45} \), primero simplificamos cada parte.
1. **Simplificación de \( \frac{180}{4 \sqrt{45}} \)**:
- Calculamos \( 4 \sqrt{45} \):
\[
\sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5}
\]
Entonces,
\[
4 \sqrt{45} = 4 \cdot 3 \sqrt{5} = 12 \sqrt{5}
\]
- Ahora sustituimos en la fracción:
\[
\frac{180}{4 \sqrt{45}} = \frac{180}{12 \sqrt{5}} = \frac{15}{\sqrt{5}}
\]
- Racionalizamos el denominador:
\[
\frac{15}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{15 \sqrt{5}}{5} = 3 \sqrt{5}
\]
2. **Simplificación de \( \frac{30}{45} \)**:
- Simplificamos la fracción:
\[
\frac{30}{45} = \frac{2}{3}
\]
3. **Sumamos ambas partes**:
- Ahora sumamos \( 3 \sqrt{5} + \frac{2}{3} \):
- Para sumar, necesitamos un denominador común. El denominador común entre 1 y 3 es 3:
\[
3 \sqrt{5} = \frac{9 \sqrt{5}}{3}
\]
- Entonces, la suma es:
\[
\frac{9 \sqrt{5}}{3} + \frac{2}{3} = \frac{9 \sqrt{5} + 2}{3}
\]
Por lo tanto, el resultado final es:
\[
a = \frac{9 \sqrt{5} + 2}{3}
\]
Quick Answer
El resultado final es \( a = \frac{9 \sqrt{5} + 2}{3} \).
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