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Answer:

[tex]\displaystyle \frac{3m^2n^2}{5(m+n)}\div \frac{12m^4n}{10(m+n)}=\displaystyle \frac{n}{2m^2}[/tex]

Step-by-step explanation:

Simplificación de expresiones algebraicas

Tenemos la expresión:

[tex]\displaystyle \frac{3m^2n^2}{5(m+n)}\div \frac{12m^4n}{10(m+n)}[/tex]

La división de fracciones suele manejarse mejor utilizando la multiplicación del inverso del denominador. Es decir, para dividir la fracción a/b entre la fracción c/d se multiplica a/b*d/c para resultar (a*d)/(b*c).

Apliquemos lo anterior al problema en consideración:

[tex]\displaystyle \frac{3m^2n^2}{5(m+n)}\div \frac{12m^4n}{10(m+n)}=\displaystyle \frac{3m^2n^2}{5(m+n)}\cdot \frac{10(m+n)}{12m^4n}[/tex]

Multiplicamos los coeficientes en el numerador y denominador y eliminamos el factor (m+n):

[tex]=\displaystyle \frac{30m^2n^2}{60m^4n}[/tex]

La potencia 2 de la m se simplifica con la potencia 4 y la potencia 2 de la n se simplifica con la potencia 1. Igualmente se simplifica la fracción numérica dividiendo entre 30:

[tex]\boxed{\displaystyle \frac{3m^2n^2}{5(m+n)}\div \frac{12m^4n}{10(m+n)}=\displaystyle \frac{n}{2m^2}}[/tex]

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​

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