Warren Kelley
06/11/2023 · Middle School
\( \therefore 3 ) y = \frac { 1 } { x ^ { 2 } } + \frac { 3 } { x ^ { 3 } } - \frac { 2 } { x } + 4 \)
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Step-by-step Solution
Para resolver la ecuación \( 3y = \frac{1}{x^2} + \frac{3}{x^3} - \frac{2}{x} + 4 \), primero podemos despejar \( y \):
\[
y = \frac{1}{3} \left( \frac{1}{x^2} + \frac{3}{x^3} - \frac{2}{x} + 4 \right)
\]
Ahora, simplificamos la expresión dentro del paréntesis:
\[
y = \frac{1}{3} \left( \frac{1}{x^2} + \frac{3}{x^3} - \frac{2}{x} + 4 \right)
\]
Para combinar los términos, podemos encontrar un denominador común. El denominador común de \( x^2 \), \( x^3 \) y \( x \) es \( x^3 \). Reescribimos cada término:
\[
y = \frac{1}{3} \left( \frac{x}{x^3} + \frac{3}{x^3} - \frac{2x^2}{x^3} + \frac{4x^3}{x^3} \right)
\]
Ahora, combinamos los términos:
\[
y = \frac{1}{3} \left( \frac{x + 3 - 2x^2 + 4x^3}{x^3} \right)
\]
Finalmente, simplificamos:
\[
y = \frac{x + 3 - 2x^2 + 4x^3}{3x^3}
\]
Por lo tanto, la expresión final para \( y \) es:
\[
y = \frac{4x^3 - 2x^2 + x + 3}{3x^3}
\]
Quick Answer
La expresión simplificada para \( y \) es \( y = \frac{4x^3 - 2x^2 + x + 3}{3x^3} \).
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